Katz Convolution and Equidistribution

Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180)
Course Book
ISBN: 978-1-4008-4270-4
Verlag: De Gruyter
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, Band 180, 208 Seiten

Reihe: Annals of Mathematics Studies

No detailed description available for "Convolution and Equidistribution".

Autoren/Hrsg.

Katz, Nicholas M.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

FrontMatter, pg. i
Contents, pg. vi
Introduction, pg. 1
CHAPTER 1. Overview, pg. 7
CHAPTER 2. Convolution of Perverse Sheaves, pg. 19
CHAPTER 3. Fibre Functors, pg. 21
CHAPTER 4. The Situation over a Finite Field, pg. 25
CHAPTER 5. Frobenius Conjugacy Classes, pg. 31
CHAPTER 6. Group-Theoretic Facts about Ggeom and Garith, pg. 33
CHAPTER 7. The Main Theorem, pg. 39
CHAPTER 8. Isogenies, Connectedness, and Lie-Irreducibility, pg. 45
CHAPTER 9. Autodualities and Signs, pg. 49
CHAPTER 10. A First Construction of Autodual Objects, pg. 53
CHAPTER 11. A Second Construction of Autodual Objects, pg. 55
CHAPTER 12. The Previous Construction in the Nonsplit Case, pg. 61
CHAPTER 13. Results of Goursat-Kolchin-Ribet Type, pg. 63
CHAPTER 14. The Case of SL(2); the Examples of Evans and Rudnick, pg. 67
CHAPTER 15. Further SL(2) Examples, Based on the Legendre Family, pg. 73
CHAPTER 16. Frobenius Tori and Weights; Getting Elements of Garith, pg. 77
CHAPTER 17. GL(n) Examples, pg. 81
CHAPTER 18. Symplectic Examples, pg. 89
CHAPTER 19. Orthogonal Examples, Especially SO(n) Examples, pg. 103
CHAPTER 20. GL(n) x GL(n) x. x GL(n) Examples, pg. 113
CHAPTER 21. SL(n) Examples, for n an Odd Prime, pg. 125
CHAPTER 22. SL(n) Examples with Slightly Composite n, pg. 135
CHAPTER 23. Other SL(n) Examples, pg. 141
CHAPTER 24. An O(2n) Example, pg. 145
CHAPTER 25. G2 Examples: the Overall Strategy, pg. 147
CHAPTER 26. G2 Examples: Construction in Characteristic Two, pg. 155
CHAPTER 27. G2 Examples: Construction in Odd Characteristic, pg. 163
CHAPTER 28. The Situation over Z: Results, pg. 173
CHAPTER 29. The Situation over Z: Questions, pg. 181
CHAPTER 30. Appendix: Deligne's Fibre Functor, pg. 187
Bibliography, pg. 193
Index, pg. 197

Über Autor(innen)

Nicholas M. Katz is professor of mathematics at Princeton University. He is the author or coauthor of six previous titles in the Annals of Mathematics Studies: Arithmetic Moduli of Elliptic Curves (with Barry Mazur); Gauss Sums, Kloosterman Sums, and Monodromy Groups; Exponential Sums and Differential Equations; Rigid Local Systems; Twisted L-Functions and Monodromy; and Moments, Monodromy, and Perversity.