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by Nicholas M. Katz
Convolution and Equidistribution
Cover Page
Title Page
Copyright
Contents
Introduction
Chapter 1. Overview
Chapter 2. Convolution of Perverse Sheaves
Chapter 3. Fibre Functors
Chapter 4. The Situation over a Finite Field
Chapter 5. Frobenius Conjugacy Classes
Chapter 6. Group-Theoretic Facts about Ggeom and Garith
Chapter 7. The Main Theorem
Chapter 8. Isogenies, Connectedness, and Lie-Irreducibility
Chapter 9. Autodualities and Signs
Chapter 10. A First Construction of Autodual Objects
Chapter 11. A Second Construction of Autodual Objects
Chapter 12. The Previous Construction in the Nonsplit Case
Chapter 13. Results of Goursat-Kolchin-Ribet Type
Chapter 14. The Case of SL(2); the Examples of Evans and Rudnick
Chapter 15. Further SL(2) Examples, Based on the Legendre Family
Chapter 16. Frobenius Tori and Weights; Getting Elements of Garith
Chapter 17. GL(n) Examples
Chapter 18. Symplectic Examples
Chapter 19. Orthogonal Examples, Especially SO(n) Examples
Chapter 20. GL(n) × GL(n) × … × GL(n) Examples
Chapter 21. SL(n) Examples, for n an Odd Prime
Chapter 22. SL(n) Examples with Slightly Composite n
Chapter 23. Other SL(n) Examples
Chapter 24. An O(2n) Example
Chapter 25. G2 Examples: the Overall Strategy
Chapter 26. G2 Examples: Construction in Characteristic Two
Chapter 27. G2 Examples: Construction in Odd Characteristic
Chapter 28. The Situation over Z: Results
Chapter 29. The Situation over Z: Questions
Chapter 30. Appendix: Deligne’s Fibre Functor
Bibliography
Index
Cover Page
Title Page
Copyright
Contents
Introduction
Chapter 1. Overview
Chapter 2. Convolution of Perverse Sheaves
Chapter 3. Fibre Functors
Chapter 4. The Situation over a Finite Field
Chapter 5. Frobenius Conjugacy Classes
Chapter 6. Group-Theoretic Facts about Ggeom and Garith
Chapter 7. The Main Theorem
Chapter 8. Isogenies, Connectedness, and Lie-Irreducibility
Chapter 9. Autodualities and Signs
Chapter 10. A First Construction of Autodual Objects
Chapter 11. A Second Construction of Autodual Objects
Chapter 12. The Previous Construction in the Nonsplit Case
Chapter 13. Results of Goursat-Kolchin-Ribet Type
Chapter 14. The Case of SL(2); the Examples of Evans and Rudnick
Chapter 15. Further SL(2) Examples, Based on the Legendre Family
Chapter 16. Frobenius Tori and Weights; Getting Elements of Garith
Chapter 17. GL(n) Examples
Chapter 18. Symplectic Examples
Chapter 19. Orthogonal Examples, Especially SO(n) Examples
Chapter 20. GL(n) × GL(n) × … × GL(n) Examples
Chapter 21. SL(n) Examples, for n an Odd Prime
Chapter 22. SL(n) Examples with Slightly Composite n
Chapter 23. Other SL(n) Examples
Chapter 24. An O(2n) Example
Chapter 25. G2 Examples: the Overall Strategy
Chapter 26. G2 Examples: Construction in Characteristic Two
Chapter 27. G2 Examples: Construction in Odd Characteristic
Chapter 28. The Situation over Z: Results
Chapter 29. The Situation over Z: Questions
Chapter 30. Appendix: Deligne’s Fibre Functor
Bibliography
Index
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Prev
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Copyright
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Convolution and Equidistribution
Contents
Introduction
Chapter 1.
Overview
Chapter 2.
Convolution of Perverse Sheaves
Chapter 3.
Fibre Functors
Chapter 4.
The Situation over a Finite Field
Chapter 5.
Frobenius Conjugacy Classes
Chapter 6.
Group-Theoretic Facts about
G
geom
and
G
arith
Chapter 7.
The Main Theorem
Chapter 8.
Isogenies, Connectedness, and Lie-Irreducibility
Chapter 9.
Autodualities and Signs
Chapter 10.
A First Construction of Autodual Objects
Chapter 11.
A Second Construction of Autodual Objects
Chapter 12.
The Previous Construction in the Nonsplit Case
Chapter 13.
Results of Goursat-Kolchin-Ribet Type
Chapter 14.
The Case of
SL
(2); the Examples of Evans and Rudnick
Chapter 15.
Further
SL
(2) Examples, Based on the Legendre Family
Chapter 16.
Frobenius Tori and Weights; Getting Elements of
G
arith
Chapter 17.
GL
(
n
) Examples
Chapter 18.
Symplectic Examples
Chapter 19.
Orthogonal Examples, Especially
SO
(
n
) Examples
Chapter 20.
GL
(
n
)
×
GL
(
n
)
× … ×
GL
(
n
) Examples
Chapter 21.
SL
(
n
) Examples, for
n
an Odd Prime
Chapter 22.
SL
(
n
) Examples with Slightly Composite
n
Chapter 23.
Other
SL
(
n
) Examples
Chapter 24.
An
O
(2
n
) Example
Chapter 25.
G
2
Examples: the Overall Strategy
Chapter 26.
G
2
Examples: Construction in Characteristic Two
Chapter 27.
G
2
Examples: Construction in Odd Characteristic
Chapter 28.
The Situation over
Z
: Results
Chapter 29.
The Situation over
Z
: Questions
Chapter 30.
Appendix: Deligne’s Fibre Functor
Bibliography
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