The geometry and cohomology of some simple Shimura varieties / Michael Harris and Richard Taylor.

Format:

Book

Author/Creator:

Harris, Michael, 1954-

Contributor:

Taylor, Richard.

Series:

Annals of mathematics studies ; no. 151.

Annals of mathematics studies ; no. 151

Language:

English

Subjects (All):

Shimura varieties.

Cohomology operations.

Physical Description:

viii, 276 pages : illustrations ; 23 cm.

Place of Publication:

Princeton, N.J. : Princeton University Press, 2002.

Contents:

I.2 Generalities on representations 21

I.3 Admissible representations of GL[subscript g] 28

I.4 Base change 37

I.5 Vanishing cycles and formal schemes 40

I.6 Involutions and unitary groups 45

I.7 Notation and running assumptions 51

II Barsotti-Tate groups 59

II.1 Barsotti-Tate groups 59

II.2 Drinfeld level structures 73

III Some simple Shimura varieties 89

III.1 Characteristic zero theory 89

III.2 Cohomology 94

III.3 The trace formula 105

III.4 Integral models 108

IV Igusa varieties 121

IV.1 Igusa varieties of the first kind 121

IV.2 Igusa varieties of the second kind 133

V Counting Points 149

V.1 An application of Fujiwara's trace formula 149

V.2 Honda-Tate theory 157

V.3 Polarisations 163

V.5 Some local harmonic analysis 182

V.6 The main theorem 191

VI Automorphic forms 195

VI.1 The Jacquet-Langlands correspondence 195

VI.2 Clozel's base change 198

VII Applications 217

VII.1 Galois representations 217

VII.2 The local Langlands conjecture 233

Appendix A result on vanishing cycles / V. G. Berkovich 257.

Notes:

Includes bibliographical references (pages 261-267) and index.

ISBN:

0691090904

0691090920

OCLC:

48065225