The Geometry and Cohomology of Some Simple Shimura Varieties.
This book aims first to prove the local Langlands conjecture for GLn over a p-adic field and, second, to identify the action of the decomposition group at a prime of bad reduction on the l-adic cohomology of the ""simple"" Shimura varieties. These two problems go hand in hand. Th...
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Full Text (via ProQuest) |
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| Format: | eBook |
| Language: | English |
| Published: |
Princeton :
Princeton University Press,
2001.
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| Series: | Annals of mathematics studies ;
no. 151. |
| Subjects: |
Table of Contents:
- Cover; Title; Copyright; Dedication; Contents; Introduction; Acknowledgements; I Preliminaries; I.1 General notation; I.2 Generalities on representations; I.3 Admissible representations of GLg; I.4 Base change; I.5 Vanishing cycles and formal schemes; I.6 Involutions and unitary groups; I.7 Notation and running assumptions; II Barsotti-Tate groups; II. 1 Barsotti-Tate groups; II. 2 Drinfeld level structures; III Some simple Shimura varieties; III. 1 Characteristic zero theory; III. 2 Cohomology; III. 3 The trace formula; III. 4 Integral models; IV Igusa varieties.
- IV. 1 Igusa varieties of the first kindIV. 2 Igusa varieties of the second kind; V Counting Points; V.1 An application of Fujiwara's trace formula; V.2 Honda-Tate theory; V.3 Polarisations I; V.4 Polarisations II; V.5 Some local harmonic analysis; V.6 The main theorem; VI Automorphic forms; VI. 1 The Jacquet-Langlands correspondence; VI. 2 Clozel's base change; VII Applications; VII. 1 Galois representations; VII. 2 The local Langlands conjecture; Appendix. A result on vanishing cycles; Bibliography; Index.