Cohomology of Drinfeld modular varieties: 1 Geometry, counting of points and local harmonic analysis
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
1996
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Cambridge studies in advanced mathematics
41 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XIII, 344 S. |
| ISBN: | 0521470609 9780521470605 9780521172745 |
Internformat
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| 245 | 1 | 0 | |a Cohomology of Drinfeld modular varieties |n 1 |p Geometry, counting of points and local harmonic analysis |c Gérard Laumon |
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| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 1996 | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface ix
1. Construction of Drinfeld modular varieties 1
(1.0) Notations 1
(1.1) Endomorphisms of the additive group 1
(1.2) Drinfeld modules 3
(1.3) Level structures 5
(1.4) Modular varieties 7
(1.5) Deformation theory 9
(1.6) Hecke algebras, correspondences 12
(1.7) Hecke operators 15
(1.8) Comments and references 18
2. Drinfeld A modules with finite characteristic 19
(2.0) Notations 19
(2.1) Isogenies 19
(2.2) Isogeny classes of Drinfeld modules 22
(2.3) Tate modules of a Drinfeld module 27
(2.4) Dieudonne modules 31
(2.5) Dieudonne module of a Drinfeld module 35
(2.6) First description of an isogeny class 43
(2.7) Isogeny classes as double coset spaces 47
(2.8) Comments and references 50
3. The Lefschetz numbers of Hecke operators 51
(3.0) Introduction 51
vi CONTENTS
(3.1) The Lefschetz numbers of correspondences 51
(3.2) Counting of fixed points 52
(3.3) Where the orbital integrals come in 56
(3.4) Transfer of conjugacy classes 60
(3.5) Transfer of Haar measures 66
(3.6) The Lefschetz numbers as sums of twisted orbital integrals 72
(3.7) Comments and references 74
4. The fundamental lemma 75
(4.0) Introduction 75
(4.1) Satake isomorphism 76
(4.2) Base change homomorphism 83
(4.3) Orbital integrals 87
(4.4) Twisted orbital integrals 93 .
(4.5) Main theorem 98
(4.6) The elliptic case 102
(4.7) The general case 114
(4.8) Non closed orbital integrals 117
(4.9) Comments and references 128
5. Very cuspidal Euler Poincare functions 129
(5.0) Introduction 129
(5.1) The function / 130
(5.2) Kottwitz s functions 133
(5.3) Elliptic orbital integrals of / 135
(5.4) if invariant constant terms of / 142
(5.5) The function / is very cuspidal 152
(5.6) Non elliptic orbital integrals of / 156
(5.7) Comments and references 156
CONTENTS vii
6. The Lefschetz numbers as sums of global elliptic orbital
integrals 158
7. Unramified principal series representations 160
(7.0) Introduction 160
(7.1) Parabolic induction and restriction 160
(7.2) Cuspidal representations 165
(7.3) Principal series representations 168
(7.4) Unramified principal series representations 178
(7.5) Spherical representations 187
(7.6) Comments and references 191
8. Euler Poincare functions as pseudocoefflcients of the
Steinberg representation 192
(8.0) Introduction 192
(8.1) The Steinberg representation 192
(8.2) Main theorem 207
(8.3) Some easy vanishing results 208
(8.4) Cohomological interpretation of tr?r(/) 213
(8.5) Unitarizable representations 220
(8.6) Proof of Howe and Moore s criterion of non unitarizability 226
(8.7) Comments and references 248
Appendices
A. Central simple algebras 249
(A.0) Central simple algebras 249
(A.I) Bicommutant theorem 250
(A.2) Central simple algebras over local fields 251
(A.3) Central simple algebras over function fields 253
(A.4) Comments and references 255
viii CONTENTS
B. Dieudonne s theory : some proofs 256
(B.I) Proof of (2.4.5) 256
(B.2) Proof of (2.4.6) 268
(B.3) Proof of (2.4.11) 272
(B.4) Comments and references 280
C. Combinatorial formulas 281
(CO) Introduction 281
(C.I) q binomial coefficients 281
D. Representations of unimodular, locally compact, totally
discontinuous, separated, topological groups 284
(D.0) Introduction 284
(D.I) Smooth representations of H 284
(D.2) Admissible representations of H 290
(D.3) Induction and restriction 292
(D.4) Cuspidal representations of H 311
(D.5) Injective and projective objects in Repa(H); cohomology 322
(D.6) Unitarizable representations 327
(D.7) Decomposition of representations into tensor products 334
(D.8) Comments and references 336
References 337
Index 341
|
| any_adam_object | 1 |
| author | Laumon, Gérard |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:55:32Z |
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| isbn | 0521470609 9780521470605 9780521172745 |
| language | English |
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| physical | XIII, 344 S. |
| publishDate | 1996 |
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| series | Cambridge studies in advanced mathematics |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Laumon, Gérard Verfasser (DE-588)121178242 aut Cohomology of Drinfeld modular varieties 1 Geometry, counting of points and local harmonic analysis Gérard Laumon 1. publ. Cambridge [u.a.] Cambridge Univ. Press 1996 XIII, 344 S. txt rdacontent n rdamedia nc rdacarrier Cambridge studies in advanced mathematics 41 Cambridge studies in advanced mathematics ... Hier auch später erschienene, unveränderte Nachdrucke Kohomologietheorie (DE-588)4164610-1 gnd rswk-swf Shimura-Mannigfaltigkeit (DE-588)4181143-4 gnd rswk-swf Spurformel (DE-588)4182612-7 gnd rswk-swf Drinfeld-Modul (DE-588)4132653-2 gnd rswk-swf Automorphe Form (DE-588)4003972-9 gnd rswk-swf Shimura-Mannigfaltigkeit (DE-588)4181143-4 s Drinfeld-Modul (DE-588)4132653-2 s Kohomologietheorie (DE-588)4164610-1 s Automorphe Form (DE-588)4003972-9 s Spurformel (DE-588)4182612-7 s DE-604 (DE-604)BV010588255 1 Cambridge studies in advanced mathematics 41 (DE-604)BV000003678 41 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007060345&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Laumon, Gérard Cohomology of Drinfeld modular varieties Cambridge studies in advanced mathematics Kohomologietheorie (DE-588)4164610-1 gnd Shimura-Mannigfaltigkeit (DE-588)4181143-4 gnd Spurformel (DE-588)4182612-7 gnd Drinfeld-Modul (DE-588)4132653-2 gnd Automorphe Form (DE-588)4003972-9 gnd |
| subject_GND | (DE-588)4164610-1 (DE-588)4181143-4 (DE-588)4182612-7 (DE-588)4132653-2 (DE-588)4003972-9 |
| title | Cohomology of Drinfeld modular varieties |
| title_auth | Cohomology of Drinfeld modular varieties |
| title_exact_search | Cohomology of Drinfeld modular varieties |
| title_full | Cohomology of Drinfeld modular varieties 1 Geometry, counting of points and local harmonic analysis Gérard Laumon |
| title_fullStr | Cohomology of Drinfeld modular varieties 1 Geometry, counting of points and local harmonic analysis Gérard Laumon |
| title_full_unstemmed | Cohomology of Drinfeld modular varieties 1 Geometry, counting of points and local harmonic analysis Gérard Laumon |
| title_short | Cohomology of Drinfeld modular varieties |
| title_sort | cohomology of drinfeld modular varieties geometry counting of points and local harmonic analysis |
| topic | Kohomologietheorie (DE-588)4164610-1 gnd Shimura-Mannigfaltigkeit (DE-588)4181143-4 gnd Spurformel (DE-588)4182612-7 gnd Drinfeld-Modul (DE-588)4132653-2 gnd Automorphe Form (DE-588)4003972-9 gnd |
| topic_facet | Kohomologietheorie Shimura-Mannigfaltigkeit Spurformel Drinfeld-Modul Automorphe Form |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007060345&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV010588255 (DE-604)BV000003678 |
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