E-Book, Englisch, Band 116, 256 Seiten
Katz Gauss Sums, Kloosterman Sums, and Monodromy Groups
1. Auflage 2016
ISBN: 978-1-4008-8212-0
Verlag: De Gruyter
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, Band 116, 256 Seiten
Reihe: Annals of Mathematics Studies
ISBN: 978-1-4008-8212-0
Verlag: De Gruyter
Format: PDF
Kopierschutz: 1 - PDF Watermark
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.
Autoren/Hrsg.
Weitere Infos & Material
Frontmatter, pg. i
Contents, pg. v
Introduction, pg. 1
CHAPTER 1. Breaks and Swan Conductors, pg. 12
CHAPTER 2. Curves and Their Cohomology, pg. 26
CHAPTER 3. Equidistribution in Equal Characteristic, pg. 36
CHAPTER 4. Gauss Sums and Kloosterman Sums: Kloosterman Sheaves, pg. 46
CHAPTER 5. Convolution of Sheaves on Gm, pg. 62
CHAPTER 6. Local Convolution, pg. 87
CHAPTER 7. Local Monodromy at Zero of a Convolution: Detailed Study, pg. 96
CHAPTER 8. Complements on Convolution, pg. 120
CHAPTER 9. Equidistribution in (S1)r of r-tuples of Angles of Gauss Sums, pg. 155
CHAPTER 10. Local Monodromy at 8 of Kloosterman Sheaves, pg. 168
CHAPTER 11. Global Monodromy of Kloosterman Sheaves, pg. 176
CHAPTER 12. Integral Monodromy of Kloosterman Sheaves (d’après O. Gabber), pg. 210
CHAPTER 13. Equidistribution of “Angles” of Kloosterman Sums, pg. 234
References, pg. 243
