Twisted L-Functions and Monodromy. (AM-150), Volume 150 / / Nicholas M. Katz.
For hundreds of years, the study of elliptic curves has played a central role in mathematics. The past century in particular has seen huge progress in this study, from Mordell's theorem in 1922 to the work of Wiles and Taylor-Wiles in 1994. Nonetheless, there remain many fundamental questions w...
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| Superior document: | Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 |
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| Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2009] ©2002 |
| Year of Publication: | 2009 |
| Edition: | Core Textbook |
| Language: | English |
| Series: | Annals of Mathematics Studies ;
150 |
| Online Access: | |
| Physical Description: | 1 online resource (264 p.) |
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Table of Contents:
- Frontmatter
- Contents
- Introduction
- Part I: Background Material
- Chapter 1: "Abstract" Theorems of Big Monodromy
- Appendix to Chapter 1: A Result of Zalesskii
- Chapter 2: Lefschetz Pencils, Especially on Curves
- Chapter 3: Induction
- Chapter 4: Middle Convolution
- Part II: Twist Sheaves, over an Algebraically Closed Field
- Chapter 5: Twist Sheaves and Their Monodromy
- Part III: Twist Sheaves, over a Finite Field
- Chapter 6: Dependence on Parameters
- Chapter 7: Diophantine Applications over a Finite Field
- Chapter 8: Average Order of Zero in Twist Families
- Part IV: Twist Sheaves, over Schemes of Finite Type over ℤ
- Chapter 9: Twisting by "Primes", and Working over ℤ
- Chapter 10: Horizontal Results
- References
- Index