Harris / Taylor The Geometry and Cohomology of Some Simple Shimura Varieties

1. Auflage 2001
ISBN: 978-1-4008-3720-5
Verlag: De Gruyter
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, Band 151, 288 Seiten

Reihe: Annals of Mathematics Studies

No detailed description available for "The Geometry and Cohomology of Some Simple Shimura Varieties".

Autoren/Hrsg.

Harris, Michael

Taylor, Richard

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

Introduction 1

Acknowledgements 15

Chapter I: Preliminaries 17

I.1 General notation 17

I.2 Generalities on representations 21

I.3 Admissible representations of GL, 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

Chapter II: Barsotti-Tate groups 59

II.1 Barsotti-Tate groups 59

II.1 Drinfeld level structures 73

Chapter III: Some simple Shimura varieties 89

III.1 Characteristic zero theory 89

III.1 Cohomology 94

III.1 The trace formula 105

III.1 Integral models 108

Chapter IV: Igusa varieties 121

IV.1 Igusa varieties of the first kind 121

IV.2 Igusa varieties of the second kind 133

Chapter V: Counting Points 149

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

V.2 Honda-Tate theory 157

V.3 Polarisations I 163

V.4 Polarisations II 168

V.5 Some local harmonic analysis 182

V.6 The main theorem 191

Chapter VI: Automorphic forms 195

VI.1 The Jacquet-Langlands correspondence 195

VI.2 Clozel's base change 198

Chapter VII: Applications 217

VII1 Galois representations 217

VII.2 The local Langlands conjecture 233

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

Bibliography 261

Index 269

Über Autor(innen)

Michael Harris is Professor of Mathematics at Université Paris 7--Denis Diderot. His research focuses on automorphic forms and representation theory, with a view to applications in number theory and arithmetical algebraic geometry. Richard Taylor is Professor of Mathematics at Harvard University. His main research interest is number theory, particularly the theory of modular forms, automorphic forms, and Galois representations.