Endoscopy for GSp(4) and the cohomology of Siegel modular threefolds:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2009
|
| Series: | Lecture notes in mathematics
1968 |
| Subjects: | |
| Online Access: | Cover Inhaltsverzeichnis |
| Physical Description: | XVII, 368 S. graph. Darst. |
| ISBN: | 9783540893059 |
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| 245 | 1 | 0 | |a Endoscopy for GSp(4) and the cohomology of Siegel modular threefolds |c Rainer Weissauer |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2009 | |
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| 490 | 1 | |a Lecture notes in mathematics |v 1968 | |
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Record in the Search Index
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| adam_text | CONTENTS 1 AN APPLICATION OF THE HART) LEFSCHETZ THEOREM 1 1.1 REVIEW OF
EICHLER INTEGRALS 1 1.2 AUTOMORPHIC REPRESENTATIONS 6 1.3 CAP AND TORIC
REPRESENTATIONS 9 1.4 THE Z-ADIC SHEAVES 11 1.5 LEFSCHETZ MAPS 12 1.6
WEAK RAMANUJAN 14 1.7 RESIDUES OF L-SERIES 15 2 CAP LOCALIZATION 19 2.1
STANDARD PARABOLIC SUBGROUPS 21 2.2 THE ADELIC REDUCTIVE BOREL-SERRE
COMPACTIFICATION 23 2.2.1 COMPONENTS 24 2.2.2 FIXED COMPONENTS H 24
2.2.3 ANOTHER FORMULATION 25 2.2.4 SMALL GROUPS 26 2.3 FIXED POINTS 27
2.3.1 ARCHIMEDEAN PLACE 28 2.3.2 NON-ARCHIMEDEAN PLACES 29 2.3.3
GLOBALLY 29 2.4 LEFSCHETZ NUMBERS 30 2.4.1 EULER CHARACTERISTICS 30
2.4.2 COMPUTATION OF O 7 32 2.4.3 CONCLUSION 32 2.5 COMPUTATION OF AN
ORBITAL INTEGTAL 34 2.6 ELLIPTIC TRACES 36 2.7 THE SATAKE TRANSFORM 38
2.7.1 SUBDIVISIONOFTHE WEYL CHAMBERS 42 2.7.2 GLOBAL SITUATION 43 2.8
AUTOMORPHIC REPRESENTATIONS 44 2.9 THE DISCRETE SERIES CASE 48
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/991010760 DIGITALISIERT
DURCH CONTENTS APPENDIX 1 50 APPENDIX 2 51 THE RAMANUJAN CONJECTURE FOR
GENUS 2 SIEGEL MODULAR FORMS 53 3.1 RESULTS OBTAINED BY KOTTWITZ, MILNE,
PINK, AND SHPIZ 56 3.1.1 STABILIZATION 58 3.2 DESTABILIZATION 60 3.3 THE
TOPOLOGICAL TRACE FORMULA 62 3.4 (G, M)-REGULARITY REMOVED 63 3.5 CAP
LOCALIZATION REVISITED 65 3.6 THE FUNDAMENTAL LEMMA 69 3.6.1 ODDS AND
ENDS 72 CHARACTER IDENTITIES AND GALOIS REPRESENTATIONS RELATED TO THE
GROUP GSP(4) 75 4.1 TECHNICAL PRELIMINARIES 76 4.1.1 REPRESENTATIONS
ATTACHED TO ER AND 5 AND P 77 4.2 GALOIS REPRESENTATIONS 78 4.2.1 THE
CLASSICAL A-ADIC REPRESENTATIONS 79 4.2.2 WEAK RECIPROCITY LAW 80 4.2.3
CM REPRESENTATIONS 81 4.3 THE TRACE FORMULA APPLIED 82 4.4 RATIONALITY
89 4.4.1 CHARACTER TRANSFER 91 4.4.2 THE LIST OF MAXIMAL F-TORIOFG 94
4.4.3 CONCEMING Q|-RATIONALITY 97 4.5 ORTHOGONALITY RELATIONS 99 4.5.1
ELLIPTIC SCALAR PRODUCTS 102 4.5.2 THE FORMULA FOR A G 102 4.5.3 INDUCED
REPRESENTATIONS 106 4.5.4 SCALAR PRODUCT FORMULA 107 4.5.5 CHARACTER
FORMULA 108 4.6 EXPONENTS AND TEMPERED REPRESENTATIONS 109 4.6. CONTENTS
4.8 SUMMARY 133 4.8.1 LIST OF IRREDUCIBLE UNITARY DISCRETE SERIES
REPRESENTATIONS OF G 135 4.9 ASYMPTOTICS 136 4.9.1 THE CHARACTER LIFT
137 4.10 WHITTAKER MODELS 144 4.10.1 THETA LIFTS 145 4.10.2 THE LOCAL
THETA LIFT 146 4.10.3 THE LOCAL L-PACKETS 149 4.11 THE ENDOSCOPIC
CHARACTER LIFT 151 4.12 THE ANISOTROPIE ENDOSCOPIC THETA LIFT 158 4.12.1
THE GLOBAL SITUATION 161 4.12.2 THE ANISOTROPIE THETA LIFT (LOCAL
THEORY) 162 4.12.3 THE JACQUET-LANGLANDS LIFT 163 4.12.4 THE
INTERTWINING MAP B 164 4.12.5 THE Q-JACQUET MODULE OF THE ANISOTROPIE
WEIL REPRESENTATION S_(A) 166 4.12.6 WHITTAKER MODELS 168 4.12.7 THE
SIEGEL PARABOLIC 169 4.12.8 THE ANISOTROPIE THETA LIFT 0- ( LOCAL AND
GLOBAL ENDOSCOPY FOR GSP(4) 175 5.1 THE LOCAL ENDOSCOPIC LIFT 175 5.1.1
THE INTEGRAL CHARACTER LIFT 177 5.1.2 STEPS (OMXI) OF THE PROOF (IN THE
P- ADIC CASE) 178 5.1.3 COMPLEMENTS ON THE LOCAL THETA LIFT 181 5.2 THE
GLOBAL SITUATION 184 5.3 THE MULTIPLICITY FORMULA 191 5.4 LOCAL AND
GLOBAL TRACE IDENTITIES 197 5.5 APPENDIX ON ARTHUR S TRACE FORMULA 203 A
SPECIAL CASE OF THE FUNDAMENTAL LEMMA 1 21 CONTENTS 6.13 THE SUMMATION
(L/F-UNRAMIFIED) 234 6.14 APPENDIX ON ORDERS (L/F-RAMIFIED) 236 6.15
APPENDIX ON ORDERS (L/F-UNRAMIFIED) 236 6.16 APPENDIX ON MEASURES 237 A
SPECIAL CASE OF THE FUNDAMENTAL LEMMA II 239 7.1 THE TOMS T 239 7.2 THE
ENDOSCOPIC GROUP M 242 7.3 ORBITAL INTEGRALS ON M 244 7.4 REDUCTION TO H
246 7.5 THE ELEMENTS OF T{F) 249 7.6 THE RESIDUE RINGS S = O E +/N F 251
7.7 INTEGRATION OVER T(F) H(F) 256 7.8 DOUBLE COSETS IN H (F) 258 7.9
SUMMATION CONDITIONS FOR V 259 7.10 RESUME 261 7.11 THE SUMMATION (F,/F
+ -RAMIFIED) 262 7.12 THE SUMMATION (E/E + -UNRAMIFIED) 263 7.13
APPENDIX I ON ORDERS ( / + -RAMIFIED) 265 7.14 APPENDIX II ON ORDERS
(F/F+-UNRAMIFIED) 265 7.15 THE GLOBAL PROPERTY 266 THE
LANGLANDS-SHELSTAD TRANSFER FACTOR 271 8.1 AN ADMISSIBLE HOMOMORPHISM
271 8.2 STATEMENT OF RESULT 276 8.2. CONTENTS XVII 9.4 THE TWISTED
FUNDAMENTAL LEMMA (UNIT ELEMENT) 297 9.4.1 THE CONDITION T^*S 298 9.4.2
THE CLASS A{T; S) 300 9.4.3 THE FROBENIUS FUNDAMENTAL LEMMA 302 9.4.4
THE SUPPORT OF O^ K 303 9.5 THE NORM MAP AND STABLE CONJUGACY 304 9.6
COMPARISON OF THE TRANSFER FACTORS A AND A E 308 9.6.1 THE FACTOR A NI
(T, 5) 309 9.6.2 THE QUOTIENT AF 7J /A/// 311 9.6.3 THE EXPLICIT
RECIPROCITY LAW 316 9.7 TWISTED TRANSFER FACTORS FOR SPLIT TORI 317 9.8
THE CASE M X ^M 319 10 REDUCTION TO UNIT ELEMENTS 321 10.1 THE
UNRAMIFIED ENDOSCOPIC LIFT 321 10.2 TWISTED TRANSFER FACTORS FOR THE
SPLIT TOMS IN MI 323 10.3 THE TWISTED SPHERICAL LIFT 324 10.3.1 THE
FROBENIUS FORMULA 326 10.3.2 THE MODIFIED TWISTED LIFT TI MOD 326 10.3.3
ELEMENTARY FUNCTIONS 328 10.3.4 SPHERICAL PROJECTORS 330 10.4 THE
(TWISTED) FUNDAMENTAL LEMMA 330 11 APPENDIX ON GALOIS COHOMOLOGY 335
11.1 EXPLICIT RECIPROCITY LAW FOR ELEMENTARY CHARACTERS 336 1
|
| any_adam_object | 1 |
| author | Weissauer, Rainer 1954- |
| author_GND | (DE-588)1051766699 |
| author_facet | Weissauer, Rainer 1954- |
| author_role | aut |
| author_sort | Weissauer, Rainer 1954- |
| author_variant | r w rw |
| building | Verbundindex |
| bvnumber | BV035440805 |
| classification_rvk | SI 850 |
| classification_tum | MAT 103f MAT 572f MAT 329f |
| ctrlnum | (OCoLC)320532681 (DE-599)DNB991010760 |
| dewey-full | 512.73 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.73 |
| dewey-search | 512.73 |
| dewey-sort | 3512.73 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV035440805 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:35:20Z |
| institution | BVB |
| isbn | 9783540893059 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017361066 |
| oclc_num | 320532681 |
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| physical | XVII, 368 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Weissauer, Rainer 1954- Verfasser (DE-588)1051766699 aut Endoscopy for GSp(4) and the cohomology of Siegel modular threefolds Rainer Weissauer Berlin [u.a.] Springer 2009 XVII, 368 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1968 Siegel-Modulform - Kohomologiegruppe - Spurformel Spurformel (DE-588)4182612-7 gnd rswk-swf Kohomologiegruppe (DE-588)4164605-8 gnd rswk-swf Siegel-Modulform (DE-588)4129460-9 gnd rswk-swf Siegel-Modulform (DE-588)4129460-9 s Kohomologiegruppe (DE-588)4164605-8 s Spurformel (DE-588)4182612-7 s DE-604 Erscheint auch als Online-Ausgabe 978-3-540-89306-6 Lecture notes in mathematics 1968 (DE-604)BV000676446 1968 DE-576;springer image/jpeg http://swbplus.bsz-bw.de/bsz305207202cov.htm 20090407020901 Cover DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017361066&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Weissauer, Rainer 1954- Endoscopy for GSp(4) and the cohomology of Siegel modular threefolds Lecture notes in mathematics Siegel-Modulform - Kohomologiegruppe - Spurformel Spurformel (DE-588)4182612-7 gnd Kohomologiegruppe (DE-588)4164605-8 gnd Siegel-Modulform (DE-588)4129460-9 gnd |
| subject_GND | (DE-588)4182612-7 (DE-588)4164605-8 (DE-588)4129460-9 |
| title | Endoscopy for GSp(4) and the cohomology of Siegel modular threefolds |
| title_auth | Endoscopy for GSp(4) and the cohomology of Siegel modular threefolds |
| title_exact_search | Endoscopy for GSp(4) and the cohomology of Siegel modular threefolds |
| title_full | Endoscopy for GSp(4) and the cohomology of Siegel modular threefolds Rainer Weissauer |
| title_fullStr | Endoscopy for GSp(4) and the cohomology of Siegel modular threefolds Rainer Weissauer |
| title_full_unstemmed | Endoscopy for GSp(4) and the cohomology of Siegel modular threefolds Rainer Weissauer |
| title_short | Endoscopy for GSp(4) and the cohomology of Siegel modular threefolds |
| title_sort | endoscopy for gsp 4 and the cohomology of siegel modular threefolds |
| topic | Siegel-Modulform - Kohomologiegruppe - Spurformel Spurformel (DE-588)4182612-7 gnd Kohomologiegruppe (DE-588)4164605-8 gnd Siegel-Modulform (DE-588)4129460-9 gnd |
| topic_facet | Siegel-Modulform - Kohomologiegruppe - Spurformel Spurformel Kohomologiegruppe Siegel-Modulform |
| url | http://swbplus.bsz-bw.de/bsz305207202cov.htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017361066&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT weissauerrainer endoscopyforgsp4andthecohomologyofsiegelmodularthreefolds |