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BL
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| Record Number
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879828
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| Main Entry
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Harris, Michael,1954-
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| Title & Author
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The Geometry and Cohomology of Some Simple Shimura Varieties. (AM-151).
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| Publication Statement
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Princeton :: Princeton University Press,, 2001.
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| Series Statement
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Annals of Mathematics Studies ;; v. 151
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| Page. NO
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1 online resource (288 pages)
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| ISBN
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0691090920
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: 1400837200
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: 9780691090924
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: 9781400837205
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| Contents
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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.
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| Abstract
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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.
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| Subject
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Shimura varieties.
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| Subject
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MATHEMATICS-- Geometry-- General.
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| Subject
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MATHEMATICS-- Number Theory.
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| Subject
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Shimura varieties.
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| Dewey Classification
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516.3/5
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| LC Classification
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QA242.5
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| Added Entry
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Taylor, R. L., (Richard Lawrence),1962-
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