内容

目次

Introduction 1 Acknowledgements 15 Chapter I: Preliminaries 17 I.1General notation 17 I.2 Generalities on representations 21 I.3 Admissiblerepresentations of GL, 28 I.4 Base change 37 I.5 Vanishing cycles andformal schemes 40 I.6 Involutions and unitary groups 45 I.7 Notation andrunning assumptions 51 Chapter II: Barsotti-Tate groups 59 II.1Barsotti-Tate groups 59 II.1 Drinfeld level structures 73 Chapter III: Somesimple Shimura varieties 89 III.1 Characteristic zero theory 89 III.1Cohomology 94 III.1 The trace formula 105 III.1 Integral models 108Chapter IV: Igusa varieties 121 IV.1 Igusa varieties of the first kind 121IV.2 Igusa varieties of the second kind 133 Chapter V: Counting Points 149V.1 An application of Ftjiwara's trace formula 149 V.2 Honda-Tate theory 157V.3 Polarisations I 163 V.4 Polarisations II 168 V.5 Some local harmonicanalysis 182 V.6 The main theorem 191 Chapter VI: Automorphic forms 195VI.1 The Jacquet-Langlands correspondence 195 VI.2 Clozel's base change 198Chapter VII: Applications 217 VII1 Galois representations 217 VII.2 Thelocal Langlands conjecture 233 Appendix. A result on vanishing cycles by V.G. Berkovich 257 Bibliography 261 Index 269