Description

Book Synopsis
In these volumes, a reader will find all of John Tate's published mathematical papers-spanning more than six decades-enriched by new comments made by the author. Included also is a selection of his letters. His letters give us a close view of how he works and of his ideas in process of formation.

Table of Contents
  • Part I: Fourier analysis in number fields and Hecke's zeta-functions by J. T. Tate
  • A note on finite ring extensions by E. Artin and J. T. Tate
  • On the relation between extremal points of convex sets and homomorphisms of algebras by J. Tate
  • Genus change in inseparable extensions of function fields by J. Tate
  • On Chevalley's proof of Luroth's theorem by S. Lang and J. Tate
  • The higher dimensional cohomology groups of class field theory by J. Tate
  • The cohomology groups of algebraic number fields by J. T. Tate
  • On the Galois cohomology of unramified extensions of function fields in one variable by Y. Kawada and J. Tate
  • On the characters of finite groups by R. Brauer and J. Tate
  • Homology of Noetherian rings and local rings by J. Tate
  • WC-groups over $p$-adic fields by J. Tate
  • On the inequality of Castelnuovo-Severi by E. Artin and J. Tate
  • On the inequality of Castelnuovo-Severi, and Hodge's theorem by J. Tate
  • Principal homogeneous spaces over abelian varieties by S. Lang and J. Tate
  • Principal homogeneous spaces for abelian varieties by J. Tate
  • A different with an odd class by A. Frohlich, J.-P. Serre, and J. Tate
  • Nilpotent quotient groups by J. Tate
  • Duality theorems in Galois cohomology over number fields by J. Tate
  • Ramification groups of local fields by S. Sen and J. Tate
  • Formal complex multiplication in local fields by J. Lubin and J. Tate
  • Algebraic cycles and poles of zeta functions by J. T. Tate
  • Elliptic curves and formal groups by J. Lubin, J. Serre, and J. Tate
  • On the conjectures of Birch and Swinnerton-Dyer and a geometric analog by J. Tate
  • Formal moduli for one-parameter formal Lie groups by J. Lubin and J. Tate
  • The cohomology groups of tori in finite Galois extensions of number fields by J. Tate
  • Global class field theory by J. T. Tate
  • Endomorphisms of abelian varieties over finite fields by J. Tate
  • The rank of elliptic curves by J. T. Tate and I. R. Safarevic
  • Residues of differentials on curves by J. Tate
  • $p$-divisible groups by J. T. Tate
  • The work of David Mumford by J. Tate
  • Classes d'isogenie des varietes abeliennes sur un corps fini (d'apres T. Honda) by J. Tate
  • Good reduction of abelian varieties by J.-P. Serre and J. Tate
  • Group schemes of prime order by J. Tate and F. Oort
  • Symbols in arithmetic by J. Tate
  • Rigid analytic spaces by J. Tate
  • The Milnor ring of a global field by H. Bass and J. Tate
  • Appendix by H. Bass and J. Tate
  • Letter from Tate to Iwasawa on a relation between $K_2$ and Galois cohomology by J. Tate
  • Points of order 13 on elliptic curves by B. Mazur and J. Tate
  • The arithmetic of elliptic curves by J. T. Tate
  • The 1974 Fields Medals (I): An algebraic geometer by J. Tate
  • Algorithm for determining the type of a singular fiber in an elliptic pencil by J. Tate
  • Letters by J. Tate
  • Part II: Problem 9: The general reciprocity law by J. Tate
  • Relations between $K_2$ and Galois cohomology by J. Tate
  • Local constants by J. T. Tate
  • On the torsion in $K_2$ of fields by J. Tate
  • Fields medals (IV): An instinct for the key idea by J. Tate
  • A simple proof of the main theorem of elimination theory in algebraic geometry by P. Cartier and J. Tate
  • Number theoretic background by J. Tate
  • The Harish-Satake transform on $GL_r$ by J. Tate
  • Brumer-Stark-Stickelberger by J. Tate
  • On conjugation of abelian varieties of CM type by J. Tate
  • On Stark's conjectures on the behavior of $L(s,\chi)$ at $s=0$ by J. Tate
  • Variation of the canonical height of a point depending on a parameter by J. Tate
  • A reciprocity law for $K_2$-traces by S. Rosset and J. Tate
  • Canonical height pairings via Biextensions by B. Mazur and J. Tate
  • On $p$-adic analogues of the conjectures of Birch and Swinnerton-Dyer by B. Mazur, J. Tate, and J. Teitelbaum
  • Refined conjectures of the ``Birch and Swinnerton-Dyer type'' by B. Mazur and J. Tate
  • Commentary on algebra by B. Gross and J. Tate
  • Some algebras associated to automorphisms of elliptic curves by M. Artin, J. Tate, and M. Van den Bergh
  • The $p$-adic sigma function by B. Mazur and J. Tate
  • Quantum deformations of $GL_n$ by M. Artin, W. Schelter, and J. Tate
  • Modules over regular algebras of dimension 3 by M. Artin, J. Tate, and M. Van den Bergh
  • Conjectures on algebraic cycles in $\ell$-adic cohomology by J. Tate
  • The center of the 3-dimensional and 4-dimensional Sklyanin algebras by S. P. Smith and J. Tate
  • The non-existence of certain Galois extensions of $\mathbb{Q}$ unramified outside 2 by J. Tate
  • The centers of 3-dimensional Sklyanin algebras by M. Artin, W. Schelter, and J. Tate
  • A review of non-Archimedean elliptic functions by J. Tate
  • Homological properties of Sklyanin algebras by J. Tate and M. Van den Bergh
  • Linear forms in $p$-adic roots of unity by J. Tate and J. F. Voloch
  • Finite flat group schemes by J. Tate
  • Bernard Dwork (1923-1998) by N. M. Katz and J. Tate
  • Galois cohomology by J. Tate
  • On a conjecture of Finotti by J. Tate
  • Refining Gross's conjecture on the values of abelian $L$-functions by J. Tate
  • On the Jacobians of plane cubics by M. Artin, F. Rodriguez-Villegas, and J. Tate
  • Computation of $p$-adic heights and log convergence by B. Mazur, W. Stein, and J. Tate
  • Letters by J. Tate

Collected Works of John Tate Parts I and II

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A Hardback by Barry Mazur, Jean-Pierre Serre

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    View other formats and editions of Collected Works of John Tate Parts I and II by Barry Mazur

    Publisher: MP-AMM American Mathematical
    Publication Date: 12/30/2016 12:00:00 AM
    ISBN13: 9780821890912, 978-0821890912
    ISBN10: 0821890913
    Also in:
    Algebraic geometry Number theory

    Description

    Book Synopsis
    In these volumes, a reader will find all of John Tate's published mathematical papers-spanning more than six decades-enriched by new comments made by the author. Included also is a selection of his letters. His letters give us a close view of how he works and of his ideas in process of formation.

    Table of Contents
    • Part I: Fourier analysis in number fields and Hecke's zeta-functions by J. T. Tate
    • A note on finite ring extensions by E. Artin and J. T. Tate
    • On the relation between extremal points of convex sets and homomorphisms of algebras by J. Tate
    • Genus change in inseparable extensions of function fields by J. Tate
    • On Chevalley's proof of Luroth's theorem by S. Lang and J. Tate
    • The higher dimensional cohomology groups of class field theory by J. Tate
    • The cohomology groups of algebraic number fields by J. T. Tate
    • On the Galois cohomology of unramified extensions of function fields in one variable by Y. Kawada and J. Tate
    • On the characters of finite groups by R. Brauer and J. Tate
    • Homology of Noetherian rings and local rings by J. Tate
    • WC-groups over $p$-adic fields by J. Tate
    • On the inequality of Castelnuovo-Severi by E. Artin and J. Tate
    • On the inequality of Castelnuovo-Severi, and Hodge's theorem by J. Tate
    • Principal homogeneous spaces over abelian varieties by S. Lang and J. Tate
    • Principal homogeneous spaces for abelian varieties by J. Tate
    • A different with an odd class by A. Frohlich, J.-P. Serre, and J. Tate
    • Nilpotent quotient groups by J. Tate
    • Duality theorems in Galois cohomology over number fields by J. Tate
    • Ramification groups of local fields by S. Sen and J. Tate
    • Formal complex multiplication in local fields by J. Lubin and J. Tate
    • Algebraic cycles and poles of zeta functions by J. T. Tate
    • Elliptic curves and formal groups by J. Lubin, J. Serre, and J. Tate
    • On the conjectures of Birch and Swinnerton-Dyer and a geometric analog by J. Tate
    • Formal moduli for one-parameter formal Lie groups by J. Lubin and J. Tate
    • The cohomology groups of tori in finite Galois extensions of number fields by J. Tate
    • Global class field theory by J. T. Tate
    • Endomorphisms of abelian varieties over finite fields by J. Tate
    • The rank of elliptic curves by J. T. Tate and I. R. Safarevic
    • Residues of differentials on curves by J. Tate
    • $p$-divisible groups by J. T. Tate
    • The work of David Mumford by J. Tate
    • Classes d'isogenie des varietes abeliennes sur un corps fini (d'apres T. Honda) by J. Tate
    • Good reduction of abelian varieties by J.-P. Serre and J. Tate
    • Group schemes of prime order by J. Tate and F. Oort
    • Symbols in arithmetic by J. Tate
    • Rigid analytic spaces by J. Tate
    • The Milnor ring of a global field by H. Bass and J. Tate
    • Appendix by H. Bass and J. Tate
    • Letter from Tate to Iwasawa on a relation between $K_2$ and Galois cohomology by J. Tate
    • Points of order 13 on elliptic curves by B. Mazur and J. Tate
    • The arithmetic of elliptic curves by J. T. Tate
    • The 1974 Fields Medals (I): An algebraic geometer by J. Tate
    • Algorithm for determining the type of a singular fiber in an elliptic pencil by J. Tate
    • Letters by J. Tate
    • Part II: Problem 9: The general reciprocity law by J. Tate
    • Relations between $K_2$ and Galois cohomology by J. Tate
    • Local constants by J. T. Tate
    • On the torsion in $K_2$ of fields by J. Tate
    • Fields medals (IV): An instinct for the key idea by J. Tate
    • A simple proof of the main theorem of elimination theory in algebraic geometry by P. Cartier and J. Tate
    • Number theoretic background by J. Tate
    • The Harish-Satake transform on $GL_r$ by J. Tate
    • Brumer-Stark-Stickelberger by J. Tate
    • On conjugation of abelian varieties of CM type by J. Tate
    • On Stark's conjectures on the behavior of $L(s,\chi)$ at $s=0$ by J. Tate
    • Variation of the canonical height of a point depending on a parameter by J. Tate
    • A reciprocity law for $K_2$-traces by S. Rosset and J. Tate
    • Canonical height pairings via Biextensions by B. Mazur and J. Tate
    • On $p$-adic analogues of the conjectures of Birch and Swinnerton-Dyer by B. Mazur, J. Tate, and J. Teitelbaum
    • Refined conjectures of the ``Birch and Swinnerton-Dyer type'' by B. Mazur and J. Tate
    • Commentary on algebra by B. Gross and J. Tate
    • Some algebras associated to automorphisms of elliptic curves by M. Artin, J. Tate, and M. Van den Bergh
    • The $p$-adic sigma function by B. Mazur and J. Tate
    • Quantum deformations of $GL_n$ by M. Artin, W. Schelter, and J. Tate
    • Modules over regular algebras of dimension 3 by M. Artin, J. Tate, and M. Van den Bergh
    • Conjectures on algebraic cycles in $\ell$-adic cohomology by J. Tate
    • The center of the 3-dimensional and 4-dimensional Sklyanin algebras by S. P. Smith and J. Tate
    • The non-existence of certain Galois extensions of $\mathbb{Q}$ unramified outside 2 by J. Tate
    • The centers of 3-dimensional Sklyanin algebras by M. Artin, W. Schelter, and J. Tate
    • A review of non-Archimedean elliptic functions by J. Tate
    • Homological properties of Sklyanin algebras by J. Tate and M. Van den Bergh
    • Linear forms in $p$-adic roots of unity by J. Tate and J. F. Voloch
    • Finite flat group schemes by J. Tate
    • Bernard Dwork (1923-1998) by N. M. Katz and J. Tate
    • Galois cohomology by J. Tate
    • On a conjecture of Finotti by J. Tate
    • Refining Gross's conjecture on the values of abelian $L$-functions by J. Tate
    • On the Jacobians of plane cubics by M. Artin, F. Rodriguez-Villegas, and J. Tate
    • Computation of $p$-adic heights and log convergence by B. Mazur, W. Stein, and J. Tate
    • Letters by J. Tate

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