| Description |
1 online resource (288 pages). |
| Physical Medium |
polychrome |
| Description |
text file |
| Series |
Annals of Mathematics Studies ; v.151
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Annals of mathematics studies.
|
| 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. |
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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. |
| Summary |
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. The results represent a major advance in algebraic number theory, finally proving the conjecture first proposed in Langlands's 1969 Washington lecture as a non-abelian generalization of local class field theory. The local Langlands conjecture for GLn(K), where K is a p-adic field, asserts. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Shimura varieties.
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Shimura varieties. |
| Genre/Form |
Electronic books.
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Electronic books.
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| Added Author |
Taylor, R. L. (Richard Lawrence), 1962-
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| Other Form: |
Print version: Harris, Michael. Geometry and Cohomology of Some Simple Shimura Varieties. (AM-151). Princeton : Princeton University Press, ©2001 9780691090924 |
| ISBN |
9781400837205 (electronic book) |
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1400837200 (electronic book) |
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