Gauss Sums, Kloosterman Sums, and Monodromy Groups. (AM-116), Volume 116

Nicholas M. Katz

Published by Princeton University Press 1988

Gauss Sums, Kloosterman Sums, and Monodromy Groups. (AM-116), Volume 116

Nicholas M. Katz

Volume 116 in the series Annals of Mathematics Studies

https://doi.org/10.1515/9781400882120

Overview
Contents

About this book

The study of exponential sums over finite fields, begun by Gauss nearly two centuries ago, has been completely transformed in recent years by advances in algebraic geometry, culminating in Deligne's work on the Weil Conjectures. It now appears as a very attractive mixture of algebraic geometry, representation theory, and the sheaf-theoretic incarnations of such standard constructions of classical analysis as convolution and Fourier transform. The book is simultaneously an account of some of these ideas, techniques, and results, and an account of their application to concrete equidistribution questions concerning Kloosterman sums and Gauss sums.

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Frontmatter Publicly Available Download PDF	i
Contents Publicly Available Download PDF	v
Introduction Requires Authentication Unlicensed Licensed Download PDF	1
CHAPTER 1. Breaks and Swan Conductors Requires Authentication Unlicensed Licensed Download PDF	12
CHAPTER 2. Curves and Their Cohomology Requires Authentication Unlicensed Licensed Download PDF	26
CHAPTER 3. Equidistribution in Equal Characteristic Requires Authentication Unlicensed Licensed Download PDF	36
CHAPTER 4. Gauss Sums and Kloosterman Sums: Kloosterman Sheaves Requires Authentication Unlicensed Licensed Download PDF	46
CHAPTER 5. Convolution of Sheaves on G_m Requires Authentication Unlicensed Licensed Download PDF	62
CHAPTER 6. Local Convolution Requires Authentication Unlicensed Licensed Download PDF	87
CHAPTER 7. Local Monodromy at Zero of a Convolution: Detailed Study Requires Authentication Unlicensed Licensed Download PDF	96
CHAPTER 8. Complements on Convolution Requires Authentication Unlicensed Licensed Download PDF	120
CHAPTER 9. Equidistribution in (S¹)^r of r-tuples of Angles of Gauss Sums Requires Authentication Unlicensed Licensed Download PDF	155
CHAPTER 10. Local Monodromy at ∞ of Kloosterman Sheaves Requires Authentication Unlicensed Licensed Download PDF	168
CHAPTER 11. Global Monodromy of Kloosterman Sheaves Requires Authentication Unlicensed Licensed Download PDF	176
CHAPTER 12. Integral Monodromy of Kloosterman Sheaves (d’après O. Gabber) Requires Authentication Unlicensed Licensed Download PDF	210
CHAPTER 13. Equidistribution of “Angles” of Kloosterman Sums Requires Authentication Unlicensed Licensed Download PDF	234
References Requires Authentication Unlicensed Licensed Download PDF	243