Mathematics Books
Princeton University Press Singular Points of Complex Hypersurfaces
Book SynopsisThe description for this book, Singular Points of Complex Hypersurfaces. (AM-61), will be forthcoming.Trade Review"John Milnor, Winner of the 2011 Abel Prize from the Norwegian Academy of Science and Letters""John Willard Milnor, Winner of the 2011 Leroy P. Steele Prize for Lifetime Achievement, American Mathematical Society"Table of Contents*Frontmatter, pg. i*PREFACE, pg. vii*CONTENTS, pg. ix* 1. INTRODUCTION, pg. 1* 2. ELEMENTARY FACTS ABOUT REAL OR COMPLEX ALGEBRAIC SETS, pg. 9* 3. THE CURVE SELECTION LEMMA, pg. 25* 4. THE FIBRATION THEOREM, pg. 33* 5. THE TOPOLOGY OF THE FIBERAND OF K, pg. 45* 6. THE CASE OF AN ISOLATED CRITICAL POINT, pg. 55* 7. THE MIDDLE BETTI NUMBER OF THE FIBER, pg. 59* 8. IS K A TOPOLOGICAL SPHERE ?, pg. 65* 9. BRIESKORN VARIETIES AND WEIGHTED HOMOGENEOUS POLYNOMIALS, pg. 71* 10. THE CLASSICAL CASE: CURVES IN C2, pg. 81* 11. A FIBRATION THEOREM FOR REAL SINGULARITIES, pg. 97*APPENDIX A. WHITNEY'S FINITENESS THEOREM FOR ALGEBRAIC SETS, pg. 105*APPENDIX B. THE MULTIPLICITY OF AN ISOLATED SOLUTION OF ANALYTIC EQUATIONS, pg. 111*BIBLIOGRAPHY, pg. 117
£51.00
Princeton University Press Generalized Feynman Amplitudes
Book SynopsisTable of Contents*Frontmatter, pg. i*Acknowledgements, pg. v*Abstract, pg. vii*tables of contents, pg. ix*Introductions, pg. 1*CHAPTER I. Renormalization in Lagrangian Field Theory, pg. 5*CHAPTER II. Definition of Generalized Amplitudes, pg. 43*CHAPTER III. Analytic Renormalization, pg. 61*CHAPTER IV. Summation of Feynman Amplitudes, pg. 81*CONCLUSION, pg. 95*APPENDIX A. Graphs, pg. 97*APPENDIX B. Distributions, pg. 103*APPENDIX C. The Free Field, pg. 109*BIBLIOGRAPHY, pg. 119
£999.99
Princeton University Press The Equidistribution Theory of Holomorphic Curves
Book SynopsisTable of Contents*Frontmatter, pg. i*PREFACE, pg. v*INTRODUCTION, pg. vii*CONTENTS, pg. xxiii*Chapter I. Generalities on projective spaces and Grassmannians, pg. 1*Chapter II. Nevanlinna theory of meromorphic functions, pg. 14*Chapter III. Elementary properties of holomorphic curves, pg. 62*Chapter IV. The two main theorems for holomorphic curves, pg. 81*Chapter V. The defect relations, pg. 147*References, pg. 217*Index of principal definitions, pg. 219
£69.70
Princeton University Press Introduction to Fourier Analysis on Euclidean
Book SynopsisPresents a treatment of basic topics that arise in Fourier analysis. This title illustrates the role played by the structure of Euclidean spaces, particularly the action of translations, dilatations, and rotations, and motivates the study of harmonic analysis on more general spaces having an analogous structure, for example, symmetric spaces.Table of Contents*Frontmatter, pg. i*Preface, pg. vii*Contents, pg. ix*I. The Fourier Transform, pg. 1*II. Boundary Values of Harmonic Functions, pg. 37*III. The Theory of Hp Spaces on Tubes, pg. 89*IV. Symmetry Properties o f the Fourier Transform, pg. 133*V. Interpolation of Operators, pg. 177*VI. Singular Integrals and Systems of Conjugate Harmonic Functions, pg. 217*VII. Multiple Fourier Series, pg. 245*Bibliography, pg. 287*Index, pg. 295
£103.70
Princeton University Press Advances in the Theory of Riemann Surfaces
Book SynopsisThe present volume contains all but two of the papers read at the conference, as well as a few papers and short notes submitted afterwards. We hope that it reflects faithfully the present state of research in the fields covered, and that it may provide an access to these fields for future investigations.Table of Contents*Frontmatter, pg. i*Preface, pg. v*Contents, pg. vii*Some Remarks on Kleinian Groups, pg. 1*Vanishing Properties of Theta Functions for Abelian Covers of Riemann Surfaces, pg. 7*Remarks on the Limit Point Set of a Finitely Generated Kleinian Group, pg. 19*Extremal Quasiconformal Mappings, pg. 27*Isomorphisms Between Teichmiiller Spaces, pg. 53*On the Mapping Class Group of Closed Surfaces as Covering Spaces, pg. 81*Schwarzian Derivatives and Mappings onto Jordan Domains, pg. 117*On the Moduli of Closed Riemann Surfaces with Symmetries, pg. 119*An Eigenvalue Problem for Riemann Surfaces, pg. 131*Relations Between Quadratic Differentials, pg. 141*Deformations of Embeddings of Riemann Surfaces in Projective Space, pg. 157*Lipschitz Mappings and the p-capacity of Rings in n-space, pg. 175*Spaces of Fuchsian Groups and Teichmulller Theory, pg. 195*On Fricke Moduli, pg. 205*Eichler Cohomology and the Structure of Finitely Generated Kleinian Groups, pg. 225*On the Degeneration of Riemann Surfaces, pg. 265*Singular Riemann Matrices, pg. 287*An Inequality for Kleinian Groups, pg. 295*On Klein's combination Theorem III, pg. 297*On Finsler Geometry and Applications to Teichmilller Spaces, pg. 317*Reproducing Formulas for Poincare Series of Dimension -2 and Applications, pg. 329*Period Relations on Riemann Surfaces, pg. 341*Schottky Implies Poincare, pg. 355*Teichmulller Mappings which Keep the Boundary Pointwise Fixed, pg. 365*Automorphisms and Isometries of Teichmilller Space, pg. 369*Deformations of Embedded Riemann Surfaces, pg. 385*Fock Representations and Theta-functions, pg. 393*Uniforrnizations of Infinitely Connected Domains, pg. 407*References, pg. 419
£85.00
Princeton University Press Introduction to Arithmetic Theory of Automorphic
Book SynopsisThe theory of automorphic forms is playing increasingly important roles in several branches of mathematics, even in physics, and is almost ubiquitous in number theory. This book introduces the reader to the subject and, in particular, to elliptic modular forms with emphasis on their number-theoretical aspects.Table of Contents* uschian groups of the first kind * Automorphic forms and functions * Hecke operators and the zeta-functions associated with modular forms * Elliptic curves * Abelian extensions of imaginary quadratic fields and complex multiplication of elliptic curves * Modular functions of higher level * Zeta-functions of algebraic curves and abelian varieties * The cohomology group assoicated with cusp forms * Arithmetic Fuschian groups
£74.80
Princeton University Press Prospects in Mathematics
Book SynopsisFive papers by distinguished American and European mathematicians describe some current trends in mathematics in the perspective of the recent past and in terms of expectations for the future. Among the subjects discussed are algebraic groups, quadratic forms, topological aspects of global analysis, variants of the index theorem, and partial differential equations.Trade ReviewJohn Willard Milnor, Winner of the 2011 Leroy P. Steele Prize for Lifetime Achievement, American Mathematical SocietyTable of Contents*Frontmatter, pg. i*PREFACE, pg. v*CONTENTS, pg. vii*THE SIGNATURE THEOREM: REMINISCENCES AND RECREATION, pg. 1*THE CALCULUS OF FOURIER INTEGRAL OPERATORS, pg. 33*SYMMETRIC INNER PRODUCTS IN CHARACTERISTIC 2, pg. 59*COHOMOLOGIE DES GROUPES DISCRETS, pg. 77*FUTURE EXTENSIONS OF INDEX THEORY AND ELLIPTIC OPERATORS, pg. 171
£59.50
Princeton University Press Lectures on PAdic LFunctions
Book SynopsisThese are notes of lectures given at Princeton University during the fall semester of 1969. The notes present an introduction to p-adic L-functions originated in Kubota-Leopoldt {10} as p-adic analogues of classical L-functions of Dirichlet.Table of Contents*Frontmatter, pg. i*PREFACE, pg. v*CONTENTS, pg. vii* 1. DIRICHLET'S L-FUNCTIONS, pg. 1* 2. GENERALIZED BERNOULLI NUMBERS, pg. 7* 3. p-ADIC L-FUNCTIONS, pg. 17* 4. p-ADIC LOGARITHMS AND p-ADIC REGULATORS, pg. 36* 5. CALCULATION OF Lp (1; chi), pg. 43* 6. AN ALTERNATE METHOD, pg. 66* 7. SOME APPLICATIONS, pg. 88*APPENDIX, pg. 100*BIBLIOGRAPHY, pg. 105
£999.99
Princeton University Press Characteristic Classes
Book SynopsisTrade Review"John Milnor, Winner of the 2011 Abel Prize from the Norwegian Academy of Science and Letters""John Willard Milnor, Winner of the 2011 Leroy P. Steele Prize for Lifetime Achievement, American Mathematical Society"Table of Contents*Frontmatter, pg. i*Preface, pg. v*Contents, pg. vii* 1. Smooth Manifolds, pg. 1* 2. Vector Bundles, pg. 13* 3. Constructing New Vector Bundles Out of Old, pg. 25* 4. Stiefel-Whitney Classes, pg. 37* 5. Grassmann Manifolds and Universal Bundles, pg. 55* 6. A Cell Structure for Grassmann Manifolds, pg. 73* 7. The Cohomology Ring H*(Gn; Z/2), pg. 83* 8. Existence of Stiefel-Whitney Classes, pg. 89* 9. Oriented Bundles and the Euler Class, pg. 95* 10. The Thom Isomorphism Theorem, pg. 105* 11. Computations in a Smooth Manifold, pg. 115* 12. Obstructions, pg. 139* 13. Complex Vector Bundles and Complex Manifolds, pg. 149* 14. Chern Classes, pg. 155* 15. Pontrjagin Classes, pg. 173* 16. Chern Numbers and Pontrjagin Numbers, pg. 183* 17. The Oriented Cobordism Ring OMEGA*, pg. 199* 18. Thom Spaces and Transversality, pg. 205* 19. Multiplicative Sequences and the Signature Theorem, pg. 219* 20. Combinatorial Pontrjagin Classes, pg. 231*Epilogue, pg. 249*Appendix A: Singular Homology and Cohomology, pg. 257*Appendix B: Bernoulli Numbers, pg. 281*Appendix C: Connections, Curvature, and Characteristic Classes, pg. 289*Bibliography, pg. 315*Index, pg. 325
£92.65
Princeton University Press Strong Rigidity of Locally Symmetric Spaces
Book SynopsisTable of Contents*Frontmatter, pg. i*Contents, pg. v* 1. Introduction, pg. 1* 2. Algebraic Preliminaries, pg. 10* 3. The Geometry of chi : Preliminaries, pg. 20* 4. A Metric Definition of the Maximal Boundary, pg. 31* 5. Polar Parts, pg. 35* 6. A Basic Inequality, pg. 44* 7. Geometry of Neighboring Flats, pg. 52* 8. Density Properties of Discrete Subgroups, pg. 62* 8. Density Properties of Discrete Subgroups, pg. 66* 10. Pseudo Isometries of Simply Connected Spaces with Negative Curvature, pg. 71* 11. Polar Regular Elements in Co-Compact GAMMA, pg. 76* 12. Pseudo-Isometric Invariance of Semi-Simple and Unipotent Elements, pg. 80* 13. The Basic Approximation, pg. 96* 14. The Map , pg. 103* 15. The Boundary Map 0, pg. 107* 16. Tits Geometries, pg. 120* 17. Rigidity for R-rank > 1, pg. 125* 18. The Restriction to Simple Groups, pg. 128* 19. Spaces of R-rank 1, pg. 134* 20. The Boundary Semi-Metric, pg. 142* 21. Quasi-Conformal Mappings Over K and Absolute Continuity on Almost All R-Circles, pg. 156* 22. The Effect of Ergodicity, pg. 169* 23. R-Rank 1 Rigidity Proof Concluded, pg. 180* 24. Concluding Remarks, pg. 187*Bibliography, pg. 193*Backmatter, pg. 197
£63.75
Princeton University Press Automorphic Forms on Adele Groups
Book SynopsisTable of Contents*Frontmatter, pg. i*PREFACE, pg. vii*CONTENTS, pg. ix* 1. THE CLASSICAL THEORY, pg. 1* 2. AUTOMORPHIC FORMS AND THE DECOMPOSITION OF L2(GAMMA\SL(2, )), pg. 22* 3. AUTOMORPHIC FORMS AS FUNCTIONS ON THE ADELE GROUP OF GL(2), pg. 40* 4. THE REPRESENTATIONS OF GL(2) OVER LOCAL AND GLOBAL FIELDS, pg. 54* 5 . CUSP FORMS AND REPRESENTATIONS OF THE ADELE GROUP OF GL(2), pg. 79* 6. HECKE THEORY FOR GL(2), pg. 98* 7 . THE CONSTRUCTION OF A SPECIAL CLASS OF AUTOMORPHIC FORMS, pg. 133* 8 . EISENSTEIN SERIES AND THE CONTINUOUS SPECTRUM, pg. 161* 9. THE TRACE FORMULA FOR GL(2), pg. 181* 10. AUTOMORPHIC FORMS ON A QUATERNION ALGEBRA, pg. 227*BIBLIOGRAPHY, pg. 260*INDEX, pg. 264
£78.20
Princeton University Press Introduction to Ergodic Theory
Book SynopsisThis monograph examines new areas of ergodic theory, describing entropy theory, elements of the renormalization group method in the theory of dynamical systems, the splitting of separatrices, and problems related to the theory of hyperbolic dynamical systems.
£59.50
Princeton University Press C8727Algebra Extensions and KHomology
Book SynopsisTable of Contents*Frontmatter, pg. i*Contents, pg. v*Preface, pg. vii*Chapter 1. An Overview, pg. 1*Chapter 2. Ext as a Group, pg. 13*Chapter 3. Ext as a Homotopy Functor, pg. 24*Chapter 4. Generalized Homology Theory and Periodicity, pg. 37*Chapter 5. Ext as K-Homology, pg. 53*Chapter 6. Index Theorems snd Novikov's Higher Signatures, pg. 64*References, pg. 76*Index, pg. 82*Index of Symbols, pg. 83*Backmatter, pg. 85
£49.30
Princeton University Press Seminar on Differential Geometry
Book SynopsisTable of Contents*Frontmatter, pg. i*TABLE OF CONTENTS, pg. v*INTRODUCTION, pg. ix*SURVEY ON PARTIAL DIFFERENTIAL EQUATIONS IN 3 DIFFERENTIAL GEOMETRY, pg. 1*POINCARE INEQUALITIES ON RIEMANNIAN MANIFOLDS, pg. 73*BONNESEN-TYPE INEQUALITIES IN ALGEBRAIC GEOMETRY, I: INTRODUCTION TO THE PROBLEM, pg. 85*LIOUVILLE THEOREMS FOR HARMONIC MAPPINGS, AND AN APPROACH TO BERNSTEIN THEOREMS, pg. 107*SUBHARMONIC FUNCTIONS, HARMONIC MAPPINGS AND ISOMETRIC IMMERSIONS, pg. 133*AN ISOPERIMETRIC INEQUALITY AND WIEDERSEHEN MANIFOLDS, pg. 143*ON THE BLASCHKE CONJECTURE, pg. 159*BEST CONSTANTS IN THE SOBOLEV IMBEDDING THEOREM THE Y AMABE PROBLEM, pg. 173*GAUSSIAN AND SCALAR CURVATURE, AN UPDATE, pg. 185*CONFORMAL METRICS WITH ZERO SCALAR CURVATURE AND A SYMMETRIZATION PROCESS VIA MAXIMUM PRINCIPLE, pg. 193*RIGIDITY OF POSITIVELY CURVED MANIFOLDS WITH LARGE DIAMETER, pg. 203*COMPLETE THREE DIMENSIONAL MANIFOLDS WITH POSITIVE RICCI CURVATURE AND SCALAR CURVATURE, pg. 209*ENTIRE SPACELIKE HYPERSURFACES OF CONSTANT MEAN CURVATURE IN MINKOWSKI SPACE, pg. 229*APPLICATIONS OF THE MONGE-AMPERE OPERATORS TO THE DIRICHLET PROBLEM FOR QUASILINEAR ELLIPTIC EQUATIONS, pg. 239*EXTREMAL KAHLER METRICS, pg. 259*L2 HARMONIC FORMS ON COMPLETE MANIFOLDS, pg. 291*L2-COHOMOLOGY AND INTERSECTION HOMOLOGY OF SINGULAR ALGEBRAIC VARIETIES, pg. 303*FUNCTION THEORY OF NONCOMPACT KAHLER MANIFOLDS OF NONPOSITIVE CURVATURE, pg. 341*KAHLER MANIFOLDS WITH VANISHING FIRST CHERN CLASS, pg. 359*COMPACTIFICATION OF NEGATIVELY CURVED COMPLETE KAHLER MANIFOLDS OF FINITE VOLUME, pg. 363*LOCAL ISOMETRIC EMBEDDINGS, pg. 381*YANG-MILLS THEORY: ITS PHYSICAL ORIGINS AND DIFFERENTIAL GEOMETRIC ASPECTS, pg. 395*SYMMETRY AND ISOLATED SINGULARITIES OF CONFORMALLY FLAT METRICS AND OF SOLUTIONS OF THE YANG-MILLS EQUATIONS, pg. 423*ON PARALLEL YANG-MILLS FIELDS, pg. 443*VARIATIONAL PROBLEMS FOR GAUGE FIELDS, pg. 455*SOME GEOMETRICAL ASPECTS OF INTEGRABLE NONLINEAR EVOLUTION EQUATIONS, pg. 465*THE CONFORMALLY INVARIANT LAPLACIAN AND THE INSTANTON VANISHING THEOREM, pg. 483*CAUSALLY DISCONNECTING SETS, MAXIMAL GEODESICS AND GEODESIC INCOMPLET-ENESS FOR STRONGLY CAUSAL SPACE-TIMES, pg. 499*RENORMALIZATION, pg. 507*METRICS WITH PRESCRIBED RICCI CURVATURE, pg. 525*BLACK HOLE UNIQUENESS THEOREMS IN CLASSICAL AND QUANTUM GRAVITY, pg. 539*GRAVITATIONAL INSTANTONS, pg. 603*SOME UNSOLVED PROBLEMS IN CLASSICAL GENERAL RELATIVITY, pg. 631*PROBLEM SECTION, pg. 669*Backmatter, pg. 707
£120.70
Princeton University Press Etale Homotopy of Simplicial Schemes
Book SynopsisTable of Contents*Frontmatter, pg. 1*INTRODUCTION, pg. 3*1. ETALE SITE OF A SIMPLICIAL SCHEME, pg. 7*2. SHEAVES AND COHOMOLOGY, pg. 13*3. COHOMOLOGY VIA HYPERCOVERINGS, pg. 20*4. ETALE TOPOLOGICAL TYPE, pg. 31*5. HOMOTOPY INVARIANTS, pg. 42*6. WEAK EQUIVALENCES, COMPLETIONS, AND HOMOTOPY LIMITS, pg. 51*7. FINITENESS AND HOMOLOGY, pg. 63*8. COMPARISON OF HOMOTOPY TYPES, pg. 70*9. APPLICATIONS TO TOPOLOGY, pg. 80*10. COMPARISON OF GEOMETRIC AND HOMOTOPY THEORETIC FIBRES, pg. 90*11. APPLICATIONS TO GEOMETRY, pg. 103*12. APPLICATIONS TO FINITE CHE VALLEY GROUPS, pg. 112*13. FUNCTION COMPLEXES, pg. 123*14. RELATIVE COHOMOLOGY, pg. 134*15. TUBULAR NEIGHBORHOODS, pg. 147*16. GENERALIZED COHOMOLOGY, pg. 158*17. POINCARE DUALITY AND LOCALLY COMPACT HOMOLOGY, pg. 170*REFERENCES, pg. 184*INDEX, pg. 188*Backmatter, pg. 191
£63.75
Princeton University Press Seminar On Minimal Submanifolds
Book SynopsisThe description for this book, Seminar On Minimal Submanifolds. (AM-103), will be forthcoming.Table of Contents*Frontmatter, pg. i*CONTENTS, pg. v*INTRODUCTION, pg. vii*SURVEY LECTURES ON MINIMAL SUBMANIFOLDS, pg. 1*ON THE EXISTENCE OF SHORT CLOSED GEODESICS AND THEIR STABILITY PROPERTIES, pg. 53*EXISTENCE OF PERIODIC MOTIONS OF CONSERVATIVE SYSTEMS, pg. 65*ARE HARMONICALLY IMMERSED SURFACES AT ALL LIKE MINIMALLY IMMERSED SURFACES?, pg. 99*ESTIMATES FOR STABLE MINIMAL SURFACE S IN THREE DIMENSIONAL MANIFOLDS, pg. 111*REGULARITY OF SIMPLY CONNECTED SURFACES WITH QUASICONFORMAL GAUSS MAP, pg. 127*CLOSED MINIMAL SURFACES IN H Y PER BOLIC 3-MANIFOLDS, pg. 147*MINIMAL SPHERES AND OTHER CONFORMAL VARIATIONAL PROBLEMS, pg. 169*MINIMAL HYPERSURFACES OF SPHERES WITH CONS TANT SCALAR CURVATURE, pg. 177*REGULAR MINIMAL HY PERSURF ACES EXIST ON MANIFOLDS IN DIMENSIONS UP TO SIX, pg. 199*AFFINE MINIMAL SURFACES, pg. 207*THE MINIMAL VARIETIES ASSOCIATED TO A CLOSED FORM, pg. 217*NECESSARY CONDITIONS FOR SUBMANIFOLDS AND CURRENTS WITH PRESCRIBED MEAN CURVATURE VECTOR, pg. 225*APPROXIMATION OF RECTIFIABLE CURRENTS BY LIPSCHITZ Q VALUED FUNCTIONS, pg. 243*SIMPLE CLOSED GEODESICS ON OVALOIDS AND THE CALCULUS OF VARIATIONS, pg. 261*ON THE GEHRING LINK PROBLEM, pg. 271*CONSTRUCTING CRYSTALLIN E MINIMAL SURFACES, pg. 275*REGULARITY OF AREA-MINIMIZING HYPERSURFACES AT BOUNDARIES WITH MULTIPLICITY, pg. 293*NEW METHODS IN THE STUDY OF FREE BOUNDARY PROBLEMS, pg. 303*SOME PROPERTIES OF CAPILLARY FREE SURFACE, pg. 323*BERNSTEIN CONJECTURE IN HYPERBOLIC GEOMETRY, pg. 339*Backmatter, pg. 359
£78.20
Princeton University Press Topics in Transcendental Algebraic Geometry
Book SynopsisThe description for this book, Topics in Transcendental Algebraic Geometry. (AM-106), will be forthcoming.Table of Contents*Frontmatter, pg. i*Table of Contents, pg. v*INTRODUCTION, pg. vii*Chapter I. VARIATION OF HODGE STRUCTURE, pg. 1*Chapter II. CURVATURE PROPERTIES OF THE HODGE BUNDLES, pg. 29*Chapter III. INFINITESIMAL VARIATION OF HODGE STRUCTURE, pg. 51*Chapter IV. ASYMPTOTIC BEHAVIOR OF A VARIATION OF HODGE STRUCTURE, pg. 63*Chapter V. MIXED HODGE STRUCTURES, COMPACTIFICATIONS AND MONODROMY WEIGHT FILTRATION, pg. 75*Chapter VI. THE CLEMENS-SCHMID EXACT SEQUENCE AND APPLICATIONS, pg. 101*Chapter VII DEGENERATION OF HODGE BUNDLES (AFTER STEENBRINK), pg. 121*Chapter VIII. INFINITESIMAL TORELLI THEOREMS AND COUNTEREXAMPLES TO TORELLI PROBLEMS, pg. 143*Chapter IX. THE TORELLI PROBLEM FOR ELLIPTIC PENCILS, pg. 157*Chapter X. THE PERIOD MAP AT THE BOUNDARY OF MODULI, pg. 183*Chapter XI. THE GENERIC TORELLI PROBLEM FOR PRYM VARIETIES AND INTERSECTIONS OF THREE QUADRICS, pg. 209*Chapter XII. INFINITESIMAL VARIATION OF HODGE STRUCTURE AND THE GENERIC GLOBAL TORELLI THEOREM, pg. 227*Chapter XIII. GENERIC TORELLI AND VARIATIONAL SCHOTTKY, pg. 239*Chapter XIV. INTERMEDIATE JACOBIANS AND NORMAL FUNCTIONS, pg. 259*Chapter XV. EXTENDABILITY OF NORMAL FUNCTIONS ASSOCIATED TO ALGEBRAIC CYCLES, pg. 269*Chapter XVI. SOME RESULTS ABOUT ABEL-JACOBI MAPPINGS, pg. 289*Chapter XVII. INFINITESIMAL INVARIANT OF NORMAL FUNCTIONS, pg. 305*Backmatter, pg. 317
£92.65
Princeton University Press Characters of Reductive Groups over a Finite
Book SynopsisThis book presents a classification of all (complex) irreducible representations of a reductive group with connected centre, over a finite field. To achieve this, the author uses etale intersection cohomology, and detailed information on representations of Weyl groups.Table of Contents*Frontmatter, pg. i*TABLE OF CONTENTS, pg. vii*INTRODUCTION, pg. ix*1. COMPUTATION OF LOCAL INTERSECTION COHOMOLOGY OF CERTAIN LINE BUNDLES OVER A SCHUBERT VARIETY, pg. 1*2. LOCAL INTERSECTION COHOMOLOGY WITH TWISTED COEFFICIENTS OF THE CLOSURES OF THE VARIETIES XW, pg. 30*3. GLOBAL INTERSECTION COHOMOLOGY WITH TWISTED COEFFICIENTS OF THE VARIETY X W, pg. 58*4. REPRESENTATIONS OF WEYL GROUPS, pg. 76*5. CELLS IN WEYL GROUPS, pg. 134*6. AN INTEGRALITY THEOREM AND A DISJOINTNESS THEOREM, pg. 180*7. SOME EXCEPTIONAL GROUPS, pg. 217*8. DECOMPOSITION OF INDUCED REPRESENTATIONS, pg. 251*9. CLASSICAL GROUPS, pg. 269*10. COMPLETION OF THE PROOF OF THEOREM 4.23, pg. 296*11. EIGENVALUES OF FROBENIUS, pg. 313*12. ON THE STRUCTURE OF LEFT CELLS, pg. 324*13. RELATIONS WITH CONJUGACY CLASSES, pg. 342*14. CONCLUDING REMARKS, pg. 351*APPENDIX, pg. 358*REFERENCES, pg. 377*SUBJECT INDEX, pg. 382*NOTATION INDEX, pg. 383*Backmatter, pg. 385
£100.30
Princeton University Press Arithmetic Moduli of Elliptic Curves
Book SynopsisTable of Contents*Frontmatter, pg. i*TABLE OF CONTENTS, pg. v*INTRODUCTION, pg. ix*Chapter 1. GENERALITIES ON " A-STRUCTURES" AND " A-GENERATORS", pg. 1*Chapter 2. REVIEW OF ELLIPTIC CURVES, pg. 63*Chapter 3. THE FOUR BASIC MODULI PROBLEMS FOR ELLIPTIC CURVES: SORITES, pg. 98*Chapter 4. THE FORMALISM OF MODULI PROBLEMS, pg. 107*Chapter 5. REGULARITY THEOREMS, pg. 129*Chapter 6. CYCLICITY, pg. 152*Chapter 7. QUOTIENTS BY FINITE GROUPS, pg. 186*Chapter 8. COARSE MODULI SCHEMES, CUSPS, AND COMPACTIFICATION, pg. 224*Chapter 9. MODULI PROBLEMS VIEWED OVER CYCLOTOMIC INTEGER RINGS, pg. 271*Chapter 1 . THE CALCULUS OF CUSPS AND COMPONENTS VIA THE GROUPS T[N], AND THE GLOBAL STRUCTURE OF THE BASIC MODULI PROBLEMS, pg. 286*Chapter 11. INTERLUDE-EXOTIC MODULAR MORPHISMS AND ISOMORPHISMS, pg. 339*Chapter 12. NEW MODULI PROBLEMS IN CHARACTERISTIC p; IGUSA CURVES, pg. 344*Chapter 13. REDUCTIONS mod p OF THE BASIC MODULI PROBLEMS, pg. 389*Chapter 14. APPLICATION TO THEOREMS OF GOOD REDUCTION, pg. 457*NOTES ADDED IN PROOF, pg. 505*REFERENCES, pg. 511
£100.30
Princeton University Press Combinatorial Group Theory and Topology
Book SynopsisTable of Contents*Frontmatter, pg. i*CONTENTS, pg. v*PREFACE, pg. vii*PROBLEMS IN COMBINATORIAL GROUP THEORY, pg. 3*POINCARE DUALITY GROUPS OF DIMENSION TWO ARE SURFACE GROUPS, pg. 35*HOW TO GENERALIZE ONE-RELATOR GROUP THEORY, pg. 53*GRAPHICAL THEORY OF AUTOMORPHISMS OF FREE GROUPS, pg. 79*PEAK REDUCTION AND AUTOMORPHISMS OF FREE GROUPS AND FREE PRODUCTS, pg. 107*NONSINGULAR EQUATIONS OF SMALL WEIGHT OVER GROUPS, pg. 121*GRAPH-THEORETIC LEMMA AND GROUP-EMBEDDINGS, pg. 145*THE TODD-COXETER PROCESS, USING GRAPHS, pg. 157*A SUBGROUP THEOREM FOR PREGROUPS, pg. 163*GROUPS WITH A RATIONAL CROSS-SECTION, pg. 175*ON THE RATIONAL GROWTH OF VIRTUALLY NILPOTENT GROUPS, pg. 185*SJOGREN'S THEOREM FOR DIMENSION SUBGROUPS - THE METABELIAN CASE, pg. 197*ON GROUP PRESENTATIONS, COPRODUCTS AND INVERSES, pg. 213*ON COMPLEXES DOMINATED BY A TWO-COMPLEX, pg. 221*SUBCOMPLEXES OF TWO-COMPLEXES AND PROJECTIVE CROSSED MODULES, pg. 255*LENGTH FUNCTIONS OF GROUP ACTIONS ON A-TREES, pg. 265*RESIDUAL FINITENESS FOR 3-MANIFOLDS, pg. 379*THE NIELSEN-THURSTON THEORY OF SURFACE AUTOMORPHISMS, pg. 397*WHITEHEAD GROUPS OF CERTAIN HYPERBOLIC MANIFOLDS, II, pg. 415*CHARACTERIZATION OF FINITE SUBGROUPS OF THE MAPPING-CLASS GROUP, pg. 433*A SEQUENCE OF PSEUDO-ANOSOV DIFFEOMORPHISMS, pg. 443*DEHN'S ALGORITHM REVISITED, WITH APPLICATIONS TO SIMPLE CURVES ON SURFACES, pg. 451*PATHS OF GEODESICS AND GEOMETRIC INTERSECTION NUMBERS: I, pg. 479*PATHS OF GEODESICS AND GEOMETRIC INTERSECTION NUMBERS: II, pg. 501*SELECTED PROBLEMS, pg. 545*Backmatter, pg. 552
£120.70
Princeton University Press Beijing Lectures in Harmonic Analysis
Book SynopsisThe purpose of this book is to describe a certain number of results involving the study of non-linear analytic dependence of some functionals arising naturally in P.D.E. or operator theory.Trade Review"This book's great strength is the analytical care with whichKavka addresses Hobbes's theories. He organizes the material bymajor issues, and his argument builds from chapter to chapter. Thewhole is a model commentary on a great philosopher's work."—Russell Hardin, University of ChicagoTable of Contents*Frontmatter, pg. i*TABLE OF CONTENTS, pg. v*PREFACE, pg. vii*NON-LINEAR HARMONIC ANALYSIS, OPERATOR THEORY AND P.D.E., pg. 1*MULTIPARAMETER FOURIER ANALYSIS, pg. 47*ELLIPTIC BOUNDARY VALUE PROBLEMS ON LIPSCHITZ DOMAINS, pg. 131*INTEGRAL FORMULAS IN COMPLEX ANALYSIS, pg. 185*VECTOR FIELDS AND NONISOTROPIC METRICS, pg. 241*OSCILLATORY INTEGRALS IN FOURIER ANALYSIS, pg. 307*AVERAGES AND SINGULAR INTEGRALS OVER LOWER DIMENSIONAL SETS, pg. 357*INDEX, pg. 423*Backmatter, pg. 425
£85.00
Princeton University Press Algebraic Topology and Algebraic KTheory
Book SynopsisThis book contains accounts of talks held at a symposium in honor of John C. Moore in October 1983 at Princeton University, The work includes papers in classical homotopy theory, homological algebra, rational homotopy theory, algebraic K-theory of spaces, and other subjects.Table of Contents*Frontmatter, pg. i*Contents, pg. vii*Preface, pg. ix*I. Exponents in Homotopy Theory, pg. 1*II. The Exponent of a Moore Space, pg. 35*III. The Space of Maps of Moore Spaces Into Spheres, pg. 72*IV. The Adams Spectral Sequence of OMEGA2S3 and Brown Gitlet Spectra, pg. 101*V. Homotopy Groups of Some Mapping Telescopes, pg. 126*VI. Mapping Telescopes and K*-Localization, pg. 152*VII. The Geometric Realization of The Chromatic Resolution, pg. 168*VIII. Equivalences Between Homotopy Theories of Diagrams, pg. 180*IX. The Role of The Steenrod Algebra in The Mod 2 Cohomology of a Finite H-Space, pg. 206*X. Maps Between Classifying Spaces, pg. 228*XI. Generic Algebras and CW Complexes, pg. 247*XII. Deformation Theory and The Little Constructions of Cartan and Moore, pg. 322*XIII. Free (Z/2)3 - Actions on Finite Complexes, pg. 332*XIV. Equivariant Constructions of Nonequivariant Spectra, pg. 345*XV. A Decomposition of The Space of Generalized Morse Functions, pg. 365*XVI. Algebriac K-Theory of Spaces, Concordance, and Stable Homotopy Theory, pg. 392*XVII. The Map BSG --> A(*) --> QS , pg. 418*XVIII. Vector Bundles, Projective Modules and The K-Theory of Spheres, pg. 432*XIX. Limits Of Infinitesimal Group Cohomology, pg. 523*XX. Algebraic K-Theory of Group Scheme Actions, pg. 539*Backmatter, pg. 564
£100.30
Princeton University Press Differential Systems and Isometric Embeddings
Book SynopsisTable of Contents*Frontmatter, pg. i*Contents, pg. vii*Preface, pg. ix*Commonly used notation, pg. xi*1. Introduction, pg. 1*2. Structure equations of Xn EN, pg. 14*3. Pfaffian differential systems, pg. 32*4. Quasi-linear Pfaffian differential system, pg. 58*5. The isometric embedding system, pg. 89*6. The characteristic variety, pg. 112*7. Isometric embeddings of space forms, pg. 156*8. Embedding Cauchy-Riemann structures, pg. 194*References, pg. 213*Index, pg. 219
£69.70
Princeton University Press Gauss Sums Kloosterman Sums and Monodromy Groups
Book SynopsisTable of Contents*Frontmatter, pg. i*Contents, pg. v*Introduction, pg. 1*CHAPTER 1. Breaks and Swan Conductors, pg. 12*CHAPTER 2. Curves and Their Cohomology, pg. 26*CHAPTER 3. Equidistribution in Equal Characteristic, pg. 36*CHAPTER 4. Gauss Sums and Kloosterman Sums: Kloosterman Sheaves, pg. 46*CHAPTER 5. Convolution of Sheaves on Gm, pg. 62*CHAPTER 6. Local Convolution, pg. 87*CHAPTER 7. Local Monodromy at Zero of a Convolution: Detailed Study, pg. 96*CHAPTER 8. Complements on Convolution, pg. 120*CHAPTER 9. Equidistribution in (S1)r of r-tuples of Angles of Gauss Sums, pg. 155*CHAPTER 10. Local Monodromy at of Kloosterman Sheaves, pg. 168*CHAPTER 11. Global Monodromy of Kloosterman Sheaves, pg. 176*CHAPTER 12. Integral Monodromy of Kloosterman Sheaves (d'apres O. Gabber), pg. 210*CHAPTER 13. Equidistribution of "Angles" of Kloosterman Sums, pg. 234*References, pg. 243
£74.80
Princeton University Press Radically Elementary Probability Theory
Book SynopsisUsing only the very elementary framework of finite probability spaces, this book treats a number of topics in the modern theory of stochastic processes. This is made possible by using a small amount of Abraham Robinson's nonstandard analysis and not attempting to convert the results into conventional form.Table of Contents*Frontmatter, pg. i*Table of contents, pg. v*Preface, pg. vii*Acknowledgments, pg. ix*1. Random variables, pg. 1*2. Algebras of random variables, pg. 6*3. Stochastic processes, pg. 10*4. External concepts, pg. 12*5. Infinitesimals, pg. 16*6. External analogues of internal notions, pg. 20*7. Properties that hold almost everywhere, pg. 25*8. L1 random variables 30, pg. 30*9. The decomposition of a stochastic process, pg. 33*10. The total variation of a process, pg. 37*11. Convergence of martingales, pg. 41*12. Fluctuations of martingales, pg. 48*13. Discontinuities of martingales, pg. 53*14. The Lindeberg condition, pg. 57*15. The maximum of a martingale, pg. 61*16. The law of large numbers, pg. 63*17. Nearly equivalent stochastic processes, pg. 72*18. The de Moivre-Laplace-Lindeberg-Feller-Wiener- Levy-Doob-Erdos-Kac-Donsker-Prokhorov theorem, pg. 75*Appendix, pg. 80*Index, pg. 95
£49.30
Princeton University Press Unitary Representations of Reductive Lie Groups
Book SynopsisBased on the "Hermann Weyl Lectures" given at the Institute for Advanced Study in January 1986. This title outlines some of what is known about irreducible unitary representations of real reductive groups, providing definitions and references, and sketches of most proofs.Table of Contents*Frontmatter, pg. i*CONTENTS, pg. vii*ACKNOWLEDGEMENTS, pg. ix*INTRODUCTION, pg. 1*Chapter 1. COMPACT GROUPS AND THE BOREL-WEIL THEOREM, pg. 19*Chapter 2. HARISH-CHANDRA MODULES, pg. 50*Chapter 3. PARABOLIC INDUCTION, pg. 62*Chapter 4. STEIN COMPLEMENTARY SERIES AND THE UNITARY DUAL OF GL(n,C), pg. 82*Chapter 5. COHOMOLOGICAL PARABOLIC INDUCTION: ANALYTIC THEORY, pg. 105*Chapter 6. COHOMOLOGICAL PARABOLIC INDUCTION: ALGEBRAIC THEORY, pg. 123*Interlude. THE IDEA OF UNIPOTENT REPRESENTATIONS, pg. 159*Chapter 7. FINITE GROUPS AND UNIPOTENT REPRESENTATIONS, pg. 164*Chapter 8. LANGLANDS' PRINCIPLE OF FUNCTORIALITY AND UNIPOTENT REPRESENTATIONS, pg. 185*Chapter 9. PRIMITIVE IDEALS AND UNIPOTENT REPRESENTATIONS, pg. 211*Chapter 10. THE ORBIT METHOD AND UNIPOTENT REPRESENTATIONS, pg. 235*Chapter 11. E-MULTIPLICITIES AND UNIPOTENT REPRESENTATIONS, pg. 258*Chapter 12. ON THE DEFINITION OF UNIPOTENT REPRESENTATIONS, pg. 284*Chapter 13. EXHAUSTION, pg. 290*REFERENCES, pg. 302*Backmatter, pg. 309
£999.99
Princeton University Press Calculus on Heisenberg Manifolds
Book SynopsisThe description for this book, Calculus on Heisenberg Manifolds. (AM-119), will be forthcoming.Table of Contents*Frontmatter, pg. i*Contents, pg. vii*Preface, pg. ix*Introduction, pg. 1*Chapter 1. The Model Operators, pg. 11*Chapter 2. Inverting the Model Operator, pg. 23*Chapter 3. Pseudodifferential Operators on Heisenberg Manifolds, pg. 80*Chapter 4. Application to the b - Complex, pg. 151*Bibliography, pg. 181*Index of Terminology, pg. 189*List of Notation, pg. 192
£63.75
Princeton University Press Simple Algebras Base Change and the Advanced
Book SynopsisStudies one of the simplest general problems in the theory, that of relating automorphic forms on arithmetic subgroups of GL(n,E) and GL(n,F) when E/F is a cyclic extension of number fields. (This is known as the base change problem for GL(n).) The problem is solved by means of the trace formula.Table of Contents*Frontmatter, pg. i*Contents, pg. v*Introduction, pg. vii*Chapter 1. Local Results, pg. 1*Chapter 2. The Global Comparison, pg. 75*Chapter 3. Base Change, pg. 199*Bibliography, pg. 225
£999.99
Princeton University Press Harmonic Analysis in Phase Space
Book SynopsisProvides a coherent account of the area of analysis that involves the Heisenberg group, quantization, the Weyl calculus, the metaplectic representation, wave packets, and related concepts. This book features: a treatment of the representations of the Heisenberg group, their associated integral transforms, and the metaplectic representation.Trade Review"[This book] is a valiant attempt to present an account of [harmonic analysis in phase space], with an emphasis on the analysis-quantum mechanics and pseudodifferential operators... The author has taken great pains to express himself clearly and ... the notation is consistent throughout... The author should be congratulated on a very valuable addition to the library of harmonic analysis."--Zentralblatt fur MathematikTable of Contents*Frontmatter, pg. i*CONTENTS, pg. v*PREFACE, pg. vii*PROLOGUE. SOME MATTERS OF NOTATION, pg. 1*CHAPTER 1. THE HEISENBERG GROUP AND ITS REPRESENTATIONS, pg. 9*CHAPTER 2. QUANTIZATION AND PSEUDODIFFERENTIAL OPERATORS, pg. 78*CHAPTER 3. WAVE PACKETS AND WAVE FRONTS, pg. 143*CHAPTER 4. THE METAPLECTIC REPRESENTATION, pg. 170*CHAPTER 5. THE OSCILLATOR SEMIGROUP, pg. 223*APPENDIX A. GAUSSIAN INTEGRALS AND A LEMMA ON DETERMINANTS, pg. 256*APPENDIX B. SOME HILBERT SPACE RESULTS, pg. 260*BIBLIOGRAPHY, pg. 265*INDEX, pg. 275
£78.20
Princeton University Press Spin Geometry
Book SynopsisThe concepts of a spin manifold, spinor fields, Dirac operators, and A-genera are presented comprehensively in this book. It also features the development of the theory of Cl-linear elliptic operators and the associated index theorem, which connects certain subtle spin-corbordism invariants to classical questions in geometry.Table of Contents*Frontmatter, pg. i*Contents, pg. vii*Preface, pg. ix*Acknowledgments, pg. xii*Introduction, pg. 1*I. Clifford Algebras, Spin Groups and Their Representations, pg. 7*II. Spin Geometry and the Dirac Operators, pg. 77*III. Index Theorems, pg. 166*IV. Applications in Geometry and Topology, pg. 278*Appendix A. Principal G-Bundles, pg. 370*Appendix B. Classifying Spaces and Characteristic Classes, pg. 376*Appendix C. Orientation Classes and Thom Isomorphisms in K-Theory, pg. 384*Appendix D. Spin'-Manifolds, pg. 390*Bibliography, pg. 402*Index, pg. 417*Notation Index, pg. 425
£133.60
Princeton University Press Elliptic Curves
Book SynopsisAn elliptic curve is a particular kind of cubic equation in two variables whose projective solutions form a group. Developing, with many examples, the elementary theory of elliptic curves, this book goes on to the subject of modular forms and the first connections with elliptic curves.
£100.30
Princeton University Press Automorphic Representation of Unitary Groups in
Book SynopsisDevelops the stable trace formula for unitary groups in three variables. This work applies the stable trace formula to obtain a classification of automorphic representations. It presents the case in which the stable trace formula has been worked out beyond the case of SL (2) and related groups.Trade Review"Reading a book like this may cause the reader to wonder when mathematics turns into art. The author has worked to create a body of knowledge which is impressive in depth and breadth and suggestive in exemplifying phenomena which transcend his special case."--Mathematical ReviewsTable of Contents*Frontmatter, pg. i*Introduction, pg. ix*Chapter 1. Preliminary definitions and notation, pg. 1*Chapter 2. The trace formula, pg. 11*Chapter 3. Stable conjugacy, pg. 19*Chapter 4. Orbital integrals and endoscopic groups, pg. 39*Chapter 5. Stabilization, pg. 68*Chapter 6. Weighted orbital integrals, pg. 79*Chapter 7. Elliptic singular terms, pg. 89*Chapter 8. Germ expansions and limit formulas, pg. 112*Chapter 9. Singularities, pg. 134*Chapter 10. The stable trace formula, pg. 153*Chapter 11. The Unitary group in two variables, pg. 161*Chapter 12. Representation theory, pg. 171*Chapter 13. Automorphic representations, pg. 198*Chapter 14. Comparison of inner forms, pg. 232*Chapter 15. Additional results, pg. 246*References, pg. 251*Subject Index, pg. 258*Notation Index, pg. 259
£999.99
Princeton University Press Exponential Sums and Differential Equations
Book SynopsisDeals with two areas of mathematics, at first sight disjoint, and with some of the analogies and interactions between them. This book discusses results about differential equations and their differential galois groups (G) and one-parameter families of exponential sums and their geometric monodromy groups (G).Table of Contents*Frontmatter, pg. i*Contents, pg. v*Introduction, pg. 1*CHAPTER 1. Results from Representation Theory, pg. 9*CHAPTER 2. D.E.'s and D-modules, pg. 31*CHAPTER 3. The Generalized Hypergeometric Equation, pg. 92*CHAPTER 4. Detailed Analysis of the Exceptional Cases, pg. 122*CHAPTER 5. Convolution of D-modules, pg. 161*CHAPTER 6. Fourier Transforms of Kummer Pullbacks of Hypergeometrics, pg. 178*CHAPTER 7. The l- adic Theory, pg. 193*CHAPTER 8. l-adic Hypergeometrics, pg. 251*CHAPTER 9. G2 Examples, Fourier Transforms, and Hypergeometrics, pg. 320*CHAPTER 10. l -adic Exceptional Cases, pg. 332*CHAPTER 11. Reductive Tannakian Categories, pg. 352*CHAPTER 12. Fourier Universality, pg. 363*CHAPTER 13. Stratifications and Convolution, pg. 384*CHAPTER 14. The Fundamental Comparison Theorems, pg. 402*References, pg. 425
£999.99
Princeton University Press Representation Theory of Semisimple Groups
Book SynopsisOffers a survey of representation theory of semisimple Lie groups. Suitable for both graduate students and researchers, this book states the theorems precisely, and gives many illustrative examples or classes of examples. It includes for the reader a useful 300-item bibliography and an extensive section of notes.Trade ReviewWinner of the 1997 Leroy P. Steele Prize, American Mathematics Society "Anthony Knapp has written a marvelous book... Written with accuracy, style, and a genuine desire to communicate the materials... This is one of the finest books I have ever had the pleasure to read, and I recommend it in the strongest possible terms to anyone wishing to appreciate the intricate beauty and technical difficulty of representation theory of semisimple Lie groups."--R. J. Plymen, Bulletin of the London Mathematical Society "Each [theme] is developed carefully and thoroughly, with beautifully worked examples and proofs that reflect long experience in teaching and research... This result is delightful: a readable text that loses almost none of its value as a reference work."--David A. Vogan Jr., Bulletin of the American Mathematical SocietyTable of ContentsPreface to the Princeton Landmarks in Mathematics Edition xiii Preface xv Acknowledgments xix CHAPTER I. SCOPE OF THE THEORY 1. The Classical Groups 3 2. Cartan Decomposition 7 3. Representations 10 4. Concrete Problems in Representation Theory 14 5. Abstract Theory for Compact Groups 14 6. Application of the Abstract Theory to Lie Groups 23 7. Problems 24 CHAPTER II. REPRESENTATIONS OF SU(2), SL(2,R), AND SL(2,C) l. The Unitary Trick 28 2. Irreducible Finite-Dimensional Complex-Linear Representations of 91(2,C) 30 3. Finite-Dimensional Representations of 91(2,C) 31 4. Irreducible Unitary Representations of SL(2,C) 33 5. Irreducible Unitary Representations of SL(2,08) 35 6. Use of SU(1,1) 39 7. Plancherel Formula 41 8. Problems 42 CHAPTER III. C VECTORS AND THE UNIVERSAL ENVELOPING ALGEBRA l. Universal Enveloping Algebra 46 2. Actions on Universal Enveloping Algebra 50 3. C Vectors 55 4. Garding Subspace. Problems 57 CHAPTER IV. REPRESENTATIONS OF COMPACT LIE GROUPS 1. Examples of Root Space Decompositions 60 2. Roots 65 3. Abstract Root Systems and Positivity 72 4. Weyl Group, Algebraically 78 5. Weights and Integral Forms 81 6. Centalizers of Tori 86 7. Theorem of the Highest Weight 89 8. Verma Modules 93 9. Weyl Group, Analytically 100 10. Weyl Character Formula 104 11. Problems 109 CHAPTER V. STRUCTURE THEORY FOR NONCOMPACT GROUPS l. Cartan Decomposition and the Unitary Trick 113 2. Iwasawa Decomposition 116 3. Regular Elements, Weyl Chambers, and the Weyl Group 121 4. Other Decompositions 126 5. Parabolic Subgroups 132 6. Integral Formulas 137 7. Borel-Weil Theorem 142 8. Problems 147 CHAPTER VI. HOLOMORPHIC DISCRETE SERIES 1. Holomorphic Discrete Series for SU(1,1) 150 2. Classical Bounded Symmetric Domains 152 3. Harish-Chandra Decomposition 153 4. Holomorphic Discrete Series 158 5. Finiteness of an Integral 161 6. Problems 164 CHAPTER VII. INDUCED REPRESENTATIONS 1. Three Pictures 167 2. Elementary Properties 169 3. Bruhat Theory 172 4. Formal Intertwining Operators 174 5. Gindikin-Karpelevic Formula 177 6. Estimates on Intertwining Operators, Part I 181 7. Analytic Continuation of Intertwining Operators, Part I 183 8. Spherical Functions 185 9. Finite-Dimensional Representations and the H function 191 10. Estimates on Intertwining Operators, Part II 196 11. Tempered Representations and Langlands Quotients 198 12. Problems 201 CHAPTER VIII. ADMISSIBLE REPRESENTATIONS l. Motivation 203 2. Admissible Representations 205 3. Invariant Subspaces 209 4. Framework for Studying Matrix Coefficients 215 5. Harish-Chandra Homomorphism 218 6. Infinitesimal Character 223 7. Differential Equations Satisfied by Matrix Coefficients 226 8. Asymptotic Expansions and Leading Exponents 234 9. First Application: Subrepresentation Theorem 238 10. Second Application: Analytic Continuation of Interwining Operators, Part II 239 11. Third Application: Control of K-Finite Z(gc)-Finite Functions 242 12. Asymptotic Expansions near the Walls 247 13. Fourth Application: Asymptotic Size of Matrix Coefficients 253 14. Fifth Application: Identification of Irreducible Tempered Representations 258 15. Sixth Application: Langlands Classification of Irreducible Admissible Representations 266 16. Problems 276 CHAPTER IX. CONSTRUCTION OF DISCRETE SERIES 1. Infinitesimally Unitary Representations 281 2. A Third Way of Treating Admissible Representations 282 3. Equivalent Definitions of Discrete Series 284 4. Motivation in General and the Construction in SU(1,1) 287 5. Finite-Dimensional Spherical Representations 300 6. Duality in the General Case 303 7. Construction of Discrete Series 309 8. Limitations on K Types 320 9. Lemma on Linear Independence 328 10. Problems 330 CHAPTER X. GLOBAL CHARACTERS l. Existence 333 2. Character Formulas for SL(2,R) 338 3. Induced Characters 347 4. Differential Equations 354 5. Analyticity on the Regular Set, Overview and Example 355 6. Analyticity on the Regular Set, General Case 360 7. Formula on the Regular Set 368 8. Behavior on the Singular Set 371 9. Families of Admissible Representations 374 10. Problems 383 CHAPTER XI. INTRODUCTION TO PLANCHEREL FORMULA l. Constructive Proof for SU(2) 385 2. Constructive Proof for SL(2,C) 387 3. Constructive Proof for SL(2,R) 394 4. Ingredients of Proof for General Case 401 5. Scheme of Proof for General Case 404 6. Properties of F f 407 7. Hirai's Patching Conditions 421 8. Problems 425 CHAPTER XII. EXHAUSTION OF DISCRETE SERIES 1. Boundedness of Numerators of Characters 426 2. Use of Patching Conditions 432 3. Formula for Discrete Series Characters 436 4. Schwartz Space 447. 5. Exhaustion of Discrete Series 452 6. Tempered Distributions 456 7. Limits of Discrete Series 460 8. Discrete Series of M 467 9. Schmid's Identity 473 10. Problems 476 CHAPTER XIII. PLANCHEREL FORMULA 1. Ideas and Ingredients 482 2. Real-Rank-One Groups, Part I 482 3. Real-Rank-One Groups, Part II 485 4. Averaged Discrete Series 494 5. Sp (2,R) 502 6. General Case 511 7. Problems 512 CHAPTER XIV. IRREDUCIBLE TEMPERED REPRESENTATIONS l. SL(2,R) from a More General Point of View 515 2. Eisenstein Integrals 520 3. Asymptotics of Eisenstein Integrals 526 4. The il Functions for Intertwining Operators 535 5. First Irreducibility Results 540 6. Normalization of Intertwining Operators and Reducibility 543 7. Connection with Plancherel Formula when dim A = 1 547 8. Harish-Chandra's Completeness Theorem 553 9. R Group 560 10. Action by Weyl Group on Representations of M 568 11. Multiplicity One Theorem 577 12. Zuckerman Tensoring of Induced Representations 584 13. Generalized Schmid Identities 587 14. Inversion of Generalized Schmid Identities 595 15. Complete Reduction of Induced Representations 599 16. Classification 606 17. Revised Langlands Classification 614 18. Problems 621 CHAPTER XV. MINIMAL K TYPES l. Definition and Formula 626 2. Inversion Problem 635 3. Connection with Intertwining Operators 641 4. Problems 647 CHAPTER XVI. UNITARY REPRESENTATIONS 1. SL(2,U8) and SL(2,C) 650 2. Continuity Arguments and Complementary Series 653 3. Criterion for Unitary Representations 655 4. Reduction to Real Infinitesimal Character 660 5. Problems 665 APPENDIX A: ELEMENTARY THEORY OF LIE GROUPS l. Lie Algebras 667 2. Structure Theory of Lie Algebras 668 3. Fundamental Group and Covering Spaces 670 4. Topological Groups 673 5. Vector Fields and Submanifolds 674 6. Lie Groups 679 APPENDIX B: REGULAR SINGULAR POINTS OF PARTIAL DIFFERENTIAL EQUATIONS 1. Summary of Classical One-Variable Theory 685 2. Uniqueness and Analytic Continuation of Solutions in Several Variables 690 3. Analog of Fundamental Matrix 693 4. Regular Singularities 697 5. Systems of Higher Order 700 6. Leading Exponents and the Analog of the Indicial Equation 703 7. Uniqueness of Representation 710 APPENDIX C: ROOTS AND RESTRICTED ROOTS FOR CLASSICAL GROUPS 1. Complex Groups 713 2. Noncompact Real Groups 713 3. Roots vs. Restricted Roots in Noncompact Real Groups 715 NOTES 719 REFERENCES 747 INDEX OF NOTATION 763 INDEX 767
£120.70
Princeton University Press The Geometry and Cohomology of Some Simple
Book SynopsisProviding instances of the local Langlands conjecture, this book aims to prove the local Langlands conjecture for GLn over a p-adic field and, to identify the action of the decomposition group at a prime of bad reduction on the l-adic cohomology of the "simple" Shimura varieties.Trade Review"...clearly and carefully written. In sum, it represents an awe-inspiring achievement and is a model of good exposition."--Bulletin of the American Mathematical Society, Volume 40, Number 2Table of ContentsIntroduction 1 Acknowledgements 15 Chapter I: Preliminaries 17 I.1 General notation 17 I.2 Generalities on representations 21 I.3 Admissible representations of GL, 28 I.4 Base change 37 I.5 Vanishing cycles and formal schemes 40 I.6 Involutions and unitary groups 45 I.7 Notation and running assumptions 51 Chapter II: Barsotti-Tate groups 59 II.1 Barsotti-Tate groups 59 II.1 Drinfeld level structures 73 Chapter III: Some simple Shimura varieties 89 III.1 Characteristic zero theory 89 III.1 Cohomology 94 III.1 The trace formula 105 III.1 Integral models 108 Chapter IV: Igusa varieties 121 IV.1 Igusa varieties of the first kind 121 IV.2 Igusa varieties of the second kind 133 Chapter V: Counting Points 149 V.1 An application of Ftjiwara's trace formula 149 V.2 Honda-Tate theory 157 V.3 Polarisations I 163 V.4 Polarisations II 168 V.5 Some local harmonic analysis 182 V.6 The main theorem 191 Chapter VI: Automorphic forms 195 VI.1 The Jacquet-Langlands correspondence 195 VI.2 Clozel's base change 198 Chapter VII: Applications 217 VII1 Galois representations 217 VII.2 The local Langlands conjecture 233 Appendix. A result on vanishing cycles by V. G. Berkovich 257 Bibliography 261 Index 269
£999.99
Princeton University Press Elementary Differential Topology
Book SynopsisThe description for this book, Elementary Differential Topology. (AM-54), will be forthcoming.Table of Contents*Frontmatter, pg. i*Preface, pg. vii*Contents, pg. xi*Chapter I. Differentiable Manifolds, pg. 1*Chapter II. Triangulations of Differentiable Manifolds, pg. 69*References, pg. 109*Index of terms, pg. 111*Backmatter, pg. 116
£46.75
Princeton University Press Mathematics in Population Biology
Book SynopsisThe formulation, analysis, and re-evaluation of mathematical models in population biology has become a valuable source of insight to mathematicians and biologists alike. This book presents an overview and selected sample of these results and ideas, organized by biological theme rather than mathematical concept.Trade ReviewMathematics in Population Biology provides a rigorous mathematical treatment of a wide variety of [models]. The attention to mathematical details is emphasized much more in this book than in many other popular mathematical biology textbooks and will be of particular interest to mathematicians... In addition, this book is an excellent reference for researchers interested in learning more about the mathematics behind the models of population biology."--Linda J. S. Allen, SIAM Review
£80.75
Princeton University Press Convergence and Uniformity in Topology
Book SynopsisThe description for this book, Convergence and Uniformity in Topology. (AM-2), will be forthcoming.Table of Contents*Frontmatter, pg. i*Introduction, pg. iii*Contents, pg. v*General Usage of The Alphabets, pg. vii*Special Usage of The Alphabets, pg. viii*Usage of General Symbols, pg. ix*Chapter I. Ordering, pg. 1*Chapter II. Direction, pg. 10*Chapter III. Convergence, pg. 16*Chapter IV. Compactness, pg. 31*Chapter V. Normality, pg. 43*Chapter VI. Structs, pg. 55*Chapter VII. Function - Spaces, pg. 71*Chapter VIII. Examples, pg. 78*Chapter IX. Discussion, pg. 82*Bibliography, pg. 87*Index, pg. 89
£40.50
Princeton University Press An Introduction to Linear Transformations in
Book SynopsisThe description for this book, An Introduction to Linear Transformations in Hilbert Space. (AM-4), will be forthcoming.Table of Contents*Frontmatter, pg. i*PREFACE, pg. v*TABLE OF CONTENTS, pg. vii*Chapter I. INTRODUCTION, pg. 1*Chapter II. HILBERT SPACE, pg. 4*Chapter III. REALIZATIONS OF HILBERT SPA, pg. 22*Chapter IV. ADDITIVE AND CLOSED TRANSFORMATIONS, pg. 31*Chapter V. WEAK CONVERGENCE, pg. 45*Chapter VI. PROJECTIONS AND ISOMETRY, pg. 51*Chapter VII . RESOLUTIONS OF THE IDENTITY, pg. 64*Chapter VIII . BOUNDED SELF-ADJOINT AND UNITARY TRANSFORMATIONS, pg. 81*Chapter IX. CANONICAL RESOLUTION AND INTEGRAL REPRESENTATIONS, pg. 95*Chapter X. SYMMETRIC OPERATORS, pg. 110*Chapter XI. REFERENCES TO FURTHER DEVELOPMENTS, pg. 122*Chapter XII. REFERENCES TO APPLICATIONS, pg. 130*REFERENCES, pg. 133
£49.30
Princeton University Press The TwoValued Iterative Systems of Mathematical
Book SynopsisThe description for this book, The Two-Valued Iterative Systems of Mathematical Logic. (AM-5), will be forthcoming.Table of Contents*Frontmatter, pg. i*CONTENTS, pg. vi*INTRODUCTION, pg. 1*Part I. PRELIMINARIES, pg. 10*PART II. DERIVATION OP CLOSED SYSTEMS, pg. 43*PART III. CO-ORDINATION AND APPLICATION, pg. 96*BIBLIOGRAPHY, pg. 119
£999.99
Princeton University Press Topics in Topology
Book SynopsisA study of the properties of manysided figures and their ability to deform, twist, and stretch without changing their shape. It offers an in-depth introduction to the field, providing explanations of what would today be considered the basic tools of algebraic topology.Table of Contents*Frontmatter, pg. i*INTRODUCTION, pg. v*TABLE OP CONTENTS, pg. vi*Chapter I. POLYTOPES, pg. 1*Chapter II. SINGULAR COMPLEXES, pg. 23*Chapter III. MAPPING AND IMBEDDING THEOREMS. RETRACTION, pg. 35*Chapter IV. LOCAL CONNECTEDNESS AND RELATED TOPICS, pg. 75*SPECIAL BIBLIOGRAPHY ON LOCAL CONNECTEDNESS AND RETRACTION, pg. 127*GENERAL BIBLIOGRAPHY, pg. 133*INDEX, pg. 136
£51.00
Princeton University Press Transcendental Numbers
Book SynopsisThe description for this book, Transcendental Numbers. (AM-16), will be forthcoming.Table of Contents*Frontmatter, pg. i*PREFACE, pg. v*CONTENTS, pg. vii*CHAPTER I. THE EXPONENTIAL FUNCTION, pg. 1*CHAPTER II. SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS, pg. 31*CHAPTER III. THE TRANSCENDENCY OF ab FOR IRRATIONAL ALGEBRAIC b AND ALGEBRAIC a <> 0, 1, pg. 75*CHAPTER IV. ELLIPTIC FUNCTIONS, pg. 85*BIBLIOGRAPHY, pg. 101*Backmatter, pg. 104
£42.50
Princeton University Press Functional Operators Volume 2 The Geometry of
Book SynopsisMeasures and integralsTable of Contents*Frontmatter, pg. i*TABLE OF CONTENTS, pg. v*CHAPTER XII. LINEAR SPACES, pg. 1*CHAPTER XIII. LINEAR OPERATORS, pg. 49*CHAPTER XIV. COMMUTATIVITY, REDUCTIBILITY, pg. 74
£46.75
Princeton University Press OrderPreserving Maps and Integration Processes
Book SynopsisThe description for this book, Order-Preserving Maps and Integration Processes. (AM-31), will be forthcoming.Table of Contents*Frontmatter, pg. i*CONTENTS, pg. v*INTRODUCTION, pg. 1*CHAPTER I. PARTIALLY ORDERED SETS AND SYSTEMS, pg. 7*CHAPTER II. DEFINITION OF THE MAPPING, pg. 36*CHAPTER III. LATTICE PROPERTIES, CONVERGENCE AND MEASURABILITY, pg. 48*CHAPTER IV. ALGEBRAIC OPERATIONS, pg. 69*CHAPTER V. REAL-VALUED FUNCTIONS, pg. 81*CHAPTER VI. APPLICATIONS, pg. 95*BIBLIOGRAPHY, pg. 135*Backmatter, pg. 138
£49.30
Princeton University Press Curvature and Betti Numbers
Book SynopsisThe description for this book, Curvature and Betti Numbers. (AM-32), will be forthcoming.Table of Contents*Frontmatter, pg. i*Preface, pg. v*Contents, pg. vii*Chapter I. Riemannian Manifold, pg. 2*Chapter II. Harmonic and Killing Vectors, pg. 26*Chapter III. Harmonic and Killing Tensors, pg. 59*Chapter IV. Harmonic and Killing Tensors in Flat Manifolds, pg. 77*Chapter V. Deviation from Flatness, pg. 81*Chapter VI. Semi-simple Group Spaces, pg. 90*Chapter VII. Pseudo-harmonic Tensors and Pseudo-Killing Tensors in Metric Manifolds with Torsion, pg. 97*Chapter VIII. Kaehler Manifold, pg. 117*Chapter IX. Supplements, pg. 170*Bibliography, pg. 187*Backmatter, pg. 192
£999.99
Princeton University Press Composition Methods in Homotopy Groups of Spheres
Book SynopsisThe description for this book, Compositional Methods in Homotopy Groups of Spheres. (AM-49), will be forthcoming.Table of Contents*Frontmatter, pg. i*Contents, pg. iv*Introduction, pg. 1*CHAPTER I. General Compositions and Secondary Compositions, pg. 5*CHAPTER II. Generalized Hopf Invariant and Secondary Compositions, pg. 16*CHAPTER III. Reduced Join and Stable Group, pg. 25*CHAPTER IV. Suspension Sequence Mod 2, pg. 34*CHAPTER V. Auxiliary Calculation of pin+k(Sn;2) for 1 <= k <= 7, pg. 39*CHAPTER VI. Some Elements Given by Secondary Compositions, pg. 51*CHAPTER VII. 2 -Primary Components of pin+k(Sn) for 8 <= k <= 13, pg. 61*CHAPTER VIII. Squaring Operations, pg. 82*CHAPTER IX. Lemmas for Generators of pin+11(Sn; 2), pg. 89*CHAPTER X. 2 -Primary Components of pin+k(Sn) for k = 14 and 15, pg. 95*CHAPTER XI. Relative J-Homomorphism, pg. 112*CHAPTER XII. 2 -Primary Components of pin+k(Sn) for 16 <= k <= 19, pg. 135*CHAPTER XIII. Odd Components, pg. 172*CHAPTER XIV. Tables, pg. 186*BIBLIOGRAPHY, pg. 192
£999.99
Princeton University Press The Essential John Nash
Book SynopsisWhen John Nash won the Nobel prize in economics in 1994, many people were surprised to learn that he was alive. This book presents Nash's contributions not only to game theory, for which he received the Nobel, but to mathematics - from Riemannian geometry and partial differential equations - in which he commands greater acclaim among academics.Trade Review"If you want to see a sugary Hollywood depiction of John Nash's life, go to the cinema. Afterwards, if you are curious about his insights, pick up a new book that explains his work and reprints his most famous papers. It is just as amazing as his personal story."--Chris Giles, Financial Times "One of the most beautifully designed economics books I have ever seen and at a low price... Why are we so intrigued by the story of John Nash? We are curious to understand a person who proves theorems we are unable to fathom. We imagine the voices from another world he has heard. We ask where he was for 30 years during which he walked among us but wasn't here. We are frightened and we are attracted by this combination of 'crazy' and 'genius', an invitation for visiting the edge of our own minds."--Ariel Rubinstein, The Times Higher Education Supplement "Any mathematician who read A Beautiful Mind ... had to be looking for the appendices--the ones explaining what Nash actually did to earn his formidable reputation within the mathematical community. Well, here they are, in a beautifully produced volume... Kuhn, Nasar, and the other contributors have performed a most welcome service by collaborating to bring together the pieces missing from A Beautiful Mind... The mathematical community is eternally in their debt."--SIAM News "The book is written in a pleasant and informal style, addressed to a large audience."--P.T. Moranu, MathematicaTable of ContentsPREFACE by Harold W. Kuhn vii INTRODUCTION by Sylvia Nasar xi Chapter 1: Press Release--The Royal Swedish Academy of Sciences 1 Chapter 2: Autobiography 5 Photo Essay 13 Editor's introduction to Chapter 3 29 Chapter 3: The Game of Hex by John Milnor 31 Editor's Introduction to Chapter 4 35 Chapter 4: The bargaining problem 37 Editor's Introduction to Chapters 5, 6, and 7 47 Chapter 5: Equilibrium Points in n-Person games 49 Chapter 6: Non-Cooperative Games Facsimile of Ph.D. Thesis 51 Chapter 7: Non-Cooperative Games 85 Chapter 8: Two-Person Coooperative Games 99 Editor's Introduction to Chapter 9 115 Chapter 9: Parallel Control 117 Chapter 10: real Algebraic Manifolds 127 Chapter 11: The Imbedding problem for Riemannian Manifolds 151 Chapter 12: Continuity of Solutions of Parabolic and Elliptic Equations 211 AFTERWORD 241 SOURCES 243
£31.50
Princeton University Press Algebraic Curves over a Finite Field
Book SynopsisPresents an introduction to the theory of algebraic curves over a finite field, a subject that has applications in areas such as finite geometry, number theory, error-correcting codes, and cryptology. This book emphasizes the algebraic geometry rather than the function field approach to algebraic curves.Trade Review"This book is well-written and I greatly enjoyed reading it. The wealth of information and examples in this book give the reader a firm foundation and develop an intuition for the subject. The authors have used it as a textbook for a two-year course, and it would be a fine introduction to any advanced undergraduate or graduate student wanting to learn this subject."--Thomas Hagedorn, MAA ReviewsTable of ContentsPreface xi PART 1. GENERAL THEORY OF CURVES 1 Chapter 1. Fundamental ideas 3 1.1 Basic definitions 3 1.2 Polynomials 6 1.3 Affine plane curves 6 1.4 Projective plane curves 9 1.5 The Hessian curve 13 1.6 Projective varieties in higher-dimensional spaces 18 1.7 Exercises 18 1.8 Notes 19 Chapter 2. Elimination theory 21 2.1 Elimination of one unknown 21 2.2 The discriminant 30 2.3 Elimination in a system in two unknowns 31 2.4 Exercises 35 2.5 Notes 36 Chapter 3. Singular points and intersections 37 3.1 The intersection number of two curves 37 3.2 B'ezout's Theorem 45 3.3 Rational and birational transformations 49 3.4 Quadratic transformations 51 3.5 Resolution of singularities 55 3.6 Exercises 61 3.7 Notes 62 Chapter 4. Branches and parametrisation 63 4.1 Formal power series 63 4.2 Branch representations 75 4.3 Branches of plane algebraic curves 81 4.4 Local quadratic transformations 84 4.5 Noether's Theorem 92 4.6 Analytic branches 99 4.7 Exercises 107 4.8 Notes 109 Chapter 5. The function field of a curve 110 5.1 Generic points 110 5.2 Rational transformations 112 5.3 Places 119 5.4 Zeros and poles 120 5.5 Separability and inseparability 122 5.6 Frobenius rational transformations 123 5.7 Derivations and differentials 125 5.8 The genus of a curve 130 5.9 Residues of differential forms 138 5.10 Higher derivatives in positive characteristic 144 5.11 The dual and bidual of a curve 155 5.12 Exercises 159 5.13 Notes 160 Chapter 6. Linear series and the Riemann-Roch Theorem 161 6.1 Divisors and linear series 161 6.2 Linear systems of curves 170 6.3 Special and non-special linear series 177 6.4 Reformulation of the Riemann-Roch Theorem 180 6.5 Some consequences of the Riemann-Roch Theorem 182 6.6 The Weierstrass Gap Theorem 184 6.7 The structure of the divisor class group 190 6.8 Exercises 196 6.9 Notes 198 Chapter 7. Algebraic curves in higher-dimensional spaces 199 7.1 Basic definitions and properties 199 7.2 Rational transformations 203 7.3 Hurwitz's Theorem 208 7.4 Linear series composed of an involution 211 7.5 The canonical curve 216 7.6 Osculating hyperplanes and ramification divisors 217 7.7 Non-classical curves and linear systems of lines 228 7.8 Non-classical curves and linear systems of conics 230 7.9 Dual curves of space curves 238 7.10 Complete linear series of small order 241 7.11 Examples of curves 254 7.12 The Linear General Position Principle 257 7.13 Castelnuovo's Bound 257 7.14 A generalisation of Clifford's Theorem 260 7.15 The Uniform Position Principle 261 7.16 Valuation rings 262 7.17 Curves as algebraic varieties of dimension one 268 7.18 Exercises 270 7.19 Notes 271 PART 2. CURVES OVER A FINITE FIELD 275 Chapter 8. Rational points and places over a finite field 277 8.1 Plane curves defined over a finite field 277 8.2 Fq-rational branches of a curve 278 8.3 Fq-rational places, divisors and linear series 281 8.4 Space curves over Fq 287 8.5 The Stohr-Voloch Theorem 292 8.6 Frobenius classicality with respect to lines 305 8.7 Frobenius classicality with respect to conics 314 8.8 The dual of a Frobenius non-classical curve 326 8.9 Exercises 327 8.10 Notes 329 Chapter 9. Zeta functions and curves with many rational points 332 9.1 The zeta function of a curve over a finite field 332 9.2 The Hasse-Weil Theorem 343 9.3 Refinements of the Hasse-Weil Theorem 348 9.4 Asymptotic bounds 353 9.5 Other estimates 356 9.6 Counting points on a plane curve 358 9.7 Further applications of the zeta function 369 9.8 The Fundamental Equation 373 9.9 Elliptic curves over Fq 378 9.10 Classification of non-singular cubics over Fq 381 9.11 Exercises 385 9.12 Notes 388 PART 3. FURTHER DEVELOPMENTS 393 Chapter 10. Maximal and optimal curves 395 10.1 Background on maximal curves 396 10.2 The Frobenius linear series of a maximal curve 399 10.3 Embedding in a Hermitian variety 407 10.4 Maximal curves lying on a quadric surface 421 10.5 Maximal curves with high genus 428 10.6 Castelnuovo's number 431 10.7 Plane maximal curves 439 10.8 Maximal curves of Hurwitz type 442 10.9 Non-isomorphic maximal curves 446 10.10 Optimal curves 447 10.11 Exercises 453 10.12 Notes 454 Chapter 11. Automorphisms of an algebraic curve 458 11.1 The action of K-automorphisms on places 459 11.2 Linear series and automorphisms 464 11.3 Automorphism groups of plane curves 468 11.4 A bound on the order of a K-automorphism 470 11.5 Automorphism groups and their fixed fields 473 11.6 The stabiliser of a place 476 11.7 Finiteness of the K-automorphism group 480 11.8 Tame automorphism groups 483 11.9 Non-tame automorphism groups 486 11.10 K-automorphism groups of particular curves 501 11.11 Fixed places of automorphisms 509 11.12 Large automorphism groups of function fields 513 11.13 K-automorphism groups fixing a place 532 11.14 Large p-subgroups fixing a place 539 11.15 Notes 542 Chapter 12. Some families of algebraic curves 546 12.1 Plane curves given by separated polynomials 546 12.2 Curves with Suzuki automorphism group 564 12.3 Curves with unitary automorphism group 572 12.4 Curves with Ree automorphism group 575 12.5 A curve attaining the Serre Bound 585 12.6 Notes 587 Chapter 13. Applications: codes and arcs 590 13.1 Algebraic-geometry codes 590 13.2 Maximum distance separable codes 594 13.3 Arcs and ovals 599 13.4 Segre's generalisation of Menelaus' Theorem 603 13.5 The connection between arcs and curves 607 13.6 Arcs in ovals in planes of even order 611 13.7 Arcs in ovals in planes of odd order 612 13.8 The second largest complete arc 615 13.9 The third largest complete arc 623 13.10 Exercises 625 13.11 Notes 625 Appendix A. Background on field theory and group theory 627 A.1 Field theory 627 A.2 Galois theory 633 A.3 Norms and traces 635 A.4 Finite fields 636 A.5 Group theory 638 A.6 Notes 649 Appendix B. Notation 650 Bibliography 655 Index 689
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