Cohomology of Drinfeld modular varieties: 2 Automorphic forms, trace formulas and Langlands correspondence
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
1997
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Cambridge studies in advanced mathematics
56 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 366 S. |
| ISBN: | 0521470617 9780521470612 9780521109901 |
Internformat
MARC
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| 245 | 1 | 0 | |a Cohomology of Drinfeld modular varieties |n 2 |p Automorphic forms, trace formulas and Langlands correspondence |c Gérard Laumon |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 1997 | |
| 300 | |a XI, 366 S. | ||
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Datensatz im Suchindex
| _version_ | 1804128103786610688 |
|---|---|
| adam_text | Contents
Preface ix
9. Trace of /a on the discrete spectrum 1
(9.0) Introduction 1
(9.1) Automorphic representations 2
(9.2) Cuspidal automorphic representations 14
(9.3) L2 automorphic representations 24
(9.4) One dimensional automorphic representations 30
(9.5) Trace of /a into the discrete spectrum 33
(9.6) Main theorem 45
(9.7) Comments and references 46
10. Non invariant Arthur trace formula: the geometric side 47
(10.0) Introduction 47
(10.1) The kernel K(h, g) 47
(10.2) Integrability of K(h, g) along the diagonal 50
(10.3) Harder s reduction theory revisited 52
(10.4) Proof of the integrability of k(g) 62
(10.5) The distributions Jgeom and Jo 71
(10.6) Kazhdan s trick 73
(10.7) The distributions Js 80
(10.8) Reduction of (10.7.6) 86
(10.9) Proof of lemma (10.8.5) 97
(10.10) Flicker Kazhdan simple trace formula 114
(10.11) Comments and references 119
vi G. LAUMON
11. Non invariant Arthur trace formula: the spectral side 120
(11.0) Introduction 120
(11.1) Arthur s truncation operators 120
(11.2) Jgeom(/) as the integral over the diagonal of the
truncated kernel 132
(11.3) Expansion of the kernel following the cuspidal data 146
(11.4) Evaluation of J^F(f) in a special case: the operators Mjv(X) 150
(11.5) Evaluation of Jj(/) in a special case: (G, M)~ families 168
(11.6) Evaluation of /J(/) in a special case: normalization of
intertwining operators 185
(11.7) Evaluation of J^F(f) in a special case: Waldspurger s theorem 195
(11.8) A simple spectral side for the trace formula 199
(11.9) Comments and references 200
12. Cohomology with compact supports of Drinfeld
modular varieties 201
(12.0) Introduction 201
(12.1) Cohomological correspondences and the Deligne conjecture 201
(12.2) Application of the Deligne conjecture to Drinfeld
modular varieties 204
(12.3) Application of the non invariant Arthur trace formula to
Drinfeld modular varieties 209
(12.4) Langlands correspondence 213
(12.5) The virtual module W| 221
(12.6) Comments and references 222
13. Intersection cohomology of Drinfeld modular
varieties: conjectures 224
(13.0) Introduction 224
(13.1) A conjectural trace formula 224
(13.2) Some particular cases of conjecture (13.1.6) 228
DRINFELD MODULAR VARIETIES vii
(13.3) A cohomological interpretation of the constants Vd (I) 242
(13.4) Intersection cohomology 244
(13.5) Comments and references 248
Appendices
D. Representations of unimodular, locally compact, totally
discontinuous, separated, topological groups: addendum 249
(D.9) Restricted tensor products 249
(D.10) Rationality properties 256
(D.ll) The Grothendieck group of admissible representations 259
(D.12) Comments and references 261
E. Reduction theory and strong approximation 262
(E.O) Introduction 262
(E.I) Reduction theory 262
(E.2) Strong approximation 272
(E.3) Comments and references 274
F. Proof of lemma (10.6.4) 275
(F.O) Notations 275
(F.I) Reductions 275
(F.2) A geometric construction 276
(F.3) The Harish Chandra lemma 277
(F.4) An application of the Harish Chandra lemma 279
(F.5) End of the proof of (10.6.4) 281
(F.6) Comments and references 282
G. The decomposition of L% following the cuspidal data 283
(G.0) Introduction 283
(G.I) Cuspidal data 283
viii G. LAUMON
(G.2) Paley Wiener functions 288
(G.3) Fourier transformation 290
(G.4) Eisenstein series 291
(G.5) Intertwining operators 299
(G.6) The constant terms of the Eisenstein series 310
(G.7) Pseudo Eisenstein series 315
(G.8) The scalar product of two pseudo Eisenstein series 320
(G.9) Analytic continuation of Eisenstein series 325
(G.10) The spectral decomposition of Lq x c for regular
cuspidal data c 329
(G.ll) Comments and references 334
References 335
Some residue computations by J. L. Waldspurger 341
Index 365
|
| any_adam_object | 1 |
| author | Laumon, Gérard |
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| author_facet | Laumon, Gérard |
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| dewey-ones | 512 - Algebra |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV013331552 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:43:56Z |
| institution | BVB |
| isbn | 0521470617 9780521470612 9780521109901 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009090275 |
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| physical | XI, 366 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| 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 2 Automorphic forms, trace formulas and Langlands correspondence Gérard Laumon 1. publ. Cambridge [u.a.] Cambridge Univ. Press 1997 XI, 366 S. txt rdacontent n rdamedia nc rdacarrier Cambridge studies in advanced mathematics 56 Cambridge studies in advanced mathematics ... Automorphe Form (DE-588)4003972-9 gnd rswk-swf Shimura-Mannigfaltigkeit (DE-588)4181143-4 gnd rswk-swf Drinfeld-Modul (DE-588)4132653-2 gnd rswk-swf Kohomologietheorie (DE-588)4164610-1 gnd rswk-swf Spurformel (DE-588)4182612-7 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 2 Cambridge studies in advanced mathematics 56 (DE-604)BV000003678 56 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009090275&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 Automorphe Form (DE-588)4003972-9 gnd Shimura-Mannigfaltigkeit (DE-588)4181143-4 gnd Drinfeld-Modul (DE-588)4132653-2 gnd Kohomologietheorie (DE-588)4164610-1 gnd Spurformel (DE-588)4182612-7 gnd |
| subject_GND | (DE-588)4003972-9 (DE-588)4181143-4 (DE-588)4132653-2 (DE-588)4164610-1 (DE-588)4182612-7 |
| 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 2 Automorphic forms, trace formulas and Langlands correspondence Gérard Laumon |
| title_fullStr | Cohomology of Drinfeld modular varieties 2 Automorphic forms, trace formulas and Langlands correspondence Gérard Laumon |
| title_full_unstemmed | Cohomology of Drinfeld modular varieties 2 Automorphic forms, trace formulas and Langlands correspondence Gérard Laumon |
| title_short | Cohomology of Drinfeld modular varieties |
| title_sort | cohomology of drinfeld modular varieties automorphic forms trace formulas and langlands correspondence |
| topic | Automorphe Form (DE-588)4003972-9 gnd Shimura-Mannigfaltigkeit (DE-588)4181143-4 gnd Drinfeld-Modul (DE-588)4132653-2 gnd Kohomologietheorie (DE-588)4164610-1 gnd Spurformel (DE-588)4182612-7 gnd |
| topic_facet | Automorphe Form Shimura-Mannigfaltigkeit Drinfeld-Modul Kohomologietheorie Spurformel |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009090275&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV010588255 (DE-604)BV000003678 |
| work_keys_str_mv | AT laumongerard cohomologyofdrinfeldmodularvarieties2 |