Description

Book Synopsis
For hundreds of years, the study of elliptic curves has played a central role in mathematics. This book explores: What is the average rank of elliptic curves, and how does the rank vary in various kinds of families of elliptic curves? It is suitable for those interested in number theory and algebraic geometry.

Table of Contents
*FrontMatter, pg. i*Contents, pg. v*Introduction, pg. 3*Chapter 1: "Abstract" Theorems of Big Monodromy, pg. 23*Appendix to Chapter 1: A Result of Zalesskii, pg. 43*Chapter 2: Lefschetz Pencils, Especially on Curves, pg. 51*Chapter 3: Induction, pg. 71*Chapter 4: Middle Convolution, pg. 79*Chapter 5: Twist Sheaves and Their Monodromy, pg. 85*Chapter 6: Dependence on Parameters, pg. 117*Chapter 7: Diophantine Applications over a Finite Field, pg. 125*Chapter 8: Average Order of Zero in Twist Families, pg. 147*Chapter 9: Twisting by "Primes", and Working over Z, pg. 179*Chapter 10: Horizontal Results, pg. 207*References, pg. 235*Index, pg. 241

Twisted LFunctions and Monodromy

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    A Paperback / softback by Nicholas M. Katz

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      Book details

      Publisher Princeton University Press
      Published 24 February 2002
      ISBN-13 9780691091518
      978-0691091518
      ISBN-10 069109151X
      Also in:
      Groups and group theory

      Description

      Book Synopsis
      For hundreds of years, the study of elliptic curves has played a central role in mathematics. This book explores: What is the average rank of elliptic curves, and how does the rank vary in various kinds of families of elliptic curves? It is suitable for those interested in number theory and algebraic geometry.

      Table of Contents
      *FrontMatter, pg. i*Contents, pg. v*Introduction, pg. 3*Chapter 1: "Abstract" Theorems of Big Monodromy, pg. 23*Appendix to Chapter 1: A Result of Zalesskii, pg. 43*Chapter 2: Lefschetz Pencils, Especially on Curves, pg. 51*Chapter 3: Induction, pg. 71*Chapter 4: Middle Convolution, pg. 79*Chapter 5: Twist Sheaves and Their Monodromy, pg. 85*Chapter 6: Dependence on Parameters, pg. 117*Chapter 7: Diophantine Applications over a Finite Field, pg. 125*Chapter 8: Average Order of Zero in Twist Families, pg. 147*Chapter 9: Twisting by "Primes", and Working over Z, pg. 179*Chapter 10: Horizontal Results, pg. 207*References, pg. 235*Index, pg. 241

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