The Geometry and Cohomology of Some Simple Shimura Varieties. (AM-151), Volume 151

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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Detalles Bibliográficos
Autor principal: Harris, Michael, 1954-
Otros Autores: Taylor, R. L. (Richard Lawrence), 1962-
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton : Princeton University Press, 2001.
Colección:Book collections on Project MUSE.
Temas:
Shimura varieties.
MATHEMATICS > Number Theory.
MATHEMATICS > Geometry > General.
Varietes de Shimura.
Electronic books.
Acceso en línea:Texto completo

MARC

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100 1 |a Harris, Michael,  |d 1954- 
245 1 4 |a The Geometry and Cohomology of Some Simple Shimura Varieties. (AM-151), Volume 151 
264 1 |a Princeton :  |b Princeton University Press,  |c 2001. 
264 3 |a Baltimore, Md. :  |b Project MUSE,   |c 0000 
264 4 |c ©2001. 
300 |a 1 online resource. 
336 |a text  |b txt  |2 rdacontent 
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490 0 |a Annals of Mathematics Studies ;  |v v. 151 
505 0 |a 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. 
505 0 |a 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. 
520 |a 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. 
546 |a In English. 
588 |a Description based on print version record. 
650 7 |a Shimura varieties.  |2 fast  |0 (OCoLC)fst01116007 
650 7 |a MATHEMATICS  |x Number Theory.  |2 bisacsh 
650 7 |a MATHEMATICS  |x Geometry  |x General.  |2 bisacsh 
650 6 |a Varietes de Shimura. 
650 0 |a Shimura varieties. 
655 7 |a Electronic books.   |2 local 
700 1 |a Taylor, R. L.  |q (Richard Lawrence),  |d 1962- 
710 2 |a Project Muse.  |e distributor 
830 0 |a Book collections on Project MUSE. 
856 4 0 |z Texto completo  |u https://projectmuse.uam.elogim.com/book/33467/ 
945 |a Project MUSE - Custom Collection 

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