Description

Book Synopsis
Develops techniques based on two ingredients: the theory of perverse sheaves and Larsen's Alternative. These techniques are then used to calculate the geometric monodromy groups attached to some specific universal families of (L-functions attached to) character sums over finite fields.

Table of Contents
Introduction 1 Chapter 1: Basic results on perversity and higher moments 9 Chapter 2: How to apply the results of Chapter 2 93 Chapter 3: Additive character sums on An 111 Chapter 4: Additive character sums on more general X 161 Chapter 5: Multiplicative character sums on An 185 Chapter 6: Middle addivitve convolution 221 Appendix A6: Swan-minimal poles 281 Chapter 7: Pullbacks to curves from A1 295 Chapter 8: One variable twists on curves 321 Chapter 9: Weierstrass sheaves as inputs 327 Chapter 10: Weirstrass families 349 Chapter 11: FJTwist families and variants 371 Chapter 12: Uniformity results 407 Chapter 13: Average analytic rank and large N limits 443 References 455 Notation Index 461 Subject Index 467

Moments Monodromy and Perversity A Diophantine

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    A Paperback / softback by Nicholas M. Katz

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      View other formats and editions of Moments Monodromy and Perversity A Diophantine by Nicholas M. Katz

      Publisher: Princeton University Press
      Publication Date: Publication Date: 02/10/2005
      ISBN13: 9780691123301, 978-0691123301
      ISBN10: 0691123306

      Description

      Book Synopsis
      Develops techniques based on two ingredients: the theory of perverse sheaves and Larsen's Alternative. These techniques are then used to calculate the geometric monodromy groups attached to some specific universal families of (L-functions attached to) character sums over finite fields.

      Table of Contents
      Introduction 1 Chapter 1: Basic results on perversity and higher moments 9 Chapter 2: How to apply the results of Chapter 2 93 Chapter 3: Additive character sums on An 111 Chapter 4: Additive character sums on more general X 161 Chapter 5: Multiplicative character sums on An 185 Chapter 6: Middle addivitve convolution 221 Appendix A6: Swan-minimal poles 281 Chapter 7: Pullbacks to curves from A1 295 Chapter 8: One variable twists on curves 321 Chapter 9: Weierstrass sheaves as inputs 327 Chapter 10: Weirstrass families 349 Chapter 11: FJTwist families and variants 371 Chapter 12: Uniformity results 407 Chapter 13: Average analytic rank and large N limits 443 References 455 Notation Index 461 Subject Index 467

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