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CHAPTER 7. The Main Theorem

Chapters in this book

  1. Frontmatter i
  2. Contents vi
  3. Introduction 1
  4. CHAPTER 1. Overview 7
  5. CHAPTER 2. Convolution of Perverse Sheaves 19
  6. CHAPTER 3. Fibre Functors 21
  7. CHAPTER 4. The Situation over a Finite Field 25
  8. CHAPTER 5. Frobenius Conjugacy Classes 31
  9. CHAPTER 6. Group-Theoretic Facts about Ggeom and Garith 33
  10. CHAPTER 7. The Main Theorem 39
  11. CHAPTER 8. Isogenies, Connectedness, and Lie-Irreducibility 45
  12. CHAPTER 9. Autodualities and Signs 49
  13. CHAPTER 10. A First Construction of Autodual Objects 53
  14. CHAPTER 11. A Second Construction of Autodual Objects 55
  15. CHAPTER 12. The Previous Construction in the Nonsplit Case 61
  16. CHAPTER 13. Results of Goursat-Kolchin-Ribet Type 63
  17. CHAPTER 14. The Case of SL(2); the Examples of Evans and Rudnick 67
  18. CHAPTER 15. Further SL(2) Examples, Based on the Legendre Family 73
  19. CHAPTER 16. Frobenius Tori and Weights; Getting Elements of Garith 77
  20. CHAPTER 17. GL(n) Examples 81
  21. CHAPTER 18. Symplectic Examples 89
  22. CHAPTER 19. Orthogonal Examples, Especially SO(n) Examples 103
  23. CHAPTER 20. GL(n) x GL(n) x ... x GL(n) Examples 113
  24. CHAPTER 21. SL(n) Examples, for n an Odd Prime 125
  25. CHAPTER 22. SL(n) Examples with Slightly Composite n 135
  26. CHAPTER 23. Other SL(n) Examples 141
  27. CHAPTER 24. An O(2n) Example 145
  28. CHAPTER 25. G2 Examples: the Overall Strategy 147
  29. CHAPTER 26. G2 Examples: Construction in Characteristic Two 155
  30. CHAPTER 27. G2 Examples: Construction in Odd Characteristic 163
  31. CHAPTER 28. The Situation over ℤ: Results 173
  32. CHAPTER 29. The Situation over ℤ: Questions 181
  33. CHAPTER 30. Appendix: Deligne's Fibre Functor 187
  34. Bibliography 193
  35. Index 197
Convolution and Equidistribution
This chapter is in the book Convolution and Equidistribution
https://doi.org/10.1515/9781400842704.39

Chapters in this book

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