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

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Bibliographic Details
Author / Creator:	Harris, Michael, 1954-
Imprint:	Princeton : Princeton University Press, 2001.
Description:	1 online resource (288 pages)
Language:	English
Series:	Annals of Mathematics Studies ; v. 151 Annals of mathematics studies.
Subject:	Shimura varieties. Shimura varieties. Electronic books.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11276078

Hidden Bibliographic Details
Other authors / contributors:	Taylor, R. L. (Richard Lawrence), 1962-
ISBN:	9781400837205 1400837200 0691090920 9780691090924
Digital file characteristics:	text file PDF
Notes:	In English. Print version record.
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.
Other form:	Print version: Harris, Michael. Geometry and Cohomology of Some Simple Shimura Varieties. (AM-151). Princeton : Princeton University Press, ©2001 9780691090924
Standard no.:	10.1515/9781400837205

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.

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