Holdings: Automorphic forms and shimura varieties of PGSp(2)

Automorphic forms and shimura varieties of PGSp(2):

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Bibliographic Details
Main Author:	Flicker, Yuval Z. (Author)
Format:	Book
Language:	English
Published:	New Jersey [u.a.] World Scientific 2005
Subjects:	Formes automorphes Shimura, Variétés de Automorphic forms Shimura varieties Projektive Gruppe Shimura-Mannigfaltigkeit Automorphe Form Symplektische Gruppe
Online Access:	Inhaltsverzeichnis
Physical Description:	XI, 324 S.
ISBN:	9812564039

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MARC


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adam_txt	AUTOMOFPHIC FORMS BY YUVAL Z FLICKER THE OHIO STATE UNIVERSITY, USA 'WORLD SCIENTIFIC NEW JERSEY * LONDON * SINGAPORE * BEIJING * SHANGHAI * HONG KONG * TAIPEI * CHENNAI CONTENTS PREFACE V ACKNOWLEDGMENT VII PART 1. LIFTING AUTOMORPHIC FORMS OF PGSP(2) TO PGL(4) 1 I. PRELIMINARIES 3 1. INTRODUCTION 3 2. STATEMENT OF RESULTS 4 3. CONJECTURAL COMPATIBILITY 28 4. CONJECTURAL RIGIDITY 30 II. BASIC FACTS 35 1. NORM MAPS 35 2. INDUCED REPRESENTATIONS 39 3. SATAKE ISOMORPHISM 46 4. INDUCED REPRESENTATIONS OF PGSP(2, F) 47 5. TWISTED CONJUGACY CLASSES 50 III. TRACE FORMULAE 60 1. TWISTED TRACE FORMULA: GEOMETRIC SIDE 60 2. TWISTED TRACE FORMULA: ANALYTIC SIDE 66 3. TRACE FORMULA OF H: SPECTRAL SIDE 73 4. TRACE FORMULA IDENTITY 78 IV. LIFTING FROM SO(4) TO PGL(4) 86 1. FROM SO(4) TO PGL(4) 86 2. SYMMETRIC SQUARE 94 3. INDUCED CASE 97 4. CUSPIDAL CASE 101 V. LIFTING FROM PGSP(2) TO PGL(4) 11 3 1. CHARACTERS ON THE SYMPLECTIC GROUP 113 2. REDUCIBILITY 119 3. TRANSFER OF DISTRIBUTIONS 122 4. ORTHOGONALITY RELATIONS 129 X CONTENTS 5. CHARACTER RELATIONS 133 6. FINE CHARACTER RELATIONS 140 7. GENERIC REPRESENTATIONS OF PGSP(2) 148 8. LOCAL LIFTING FROM PGSP(2) 152 9. LOCAL PACKETS 160 10. GLOBAL PACKETS 161 11., REPRESENTATIONS OF PGSP(2, R) 174 VI. FUNDAMENTAL LEMMA 182 1. CASE OF SL(2) 182 2. CASE OF GSP(2) 184 PART 2. ZETA FUNCTIONS OF SHIMURA VARIETIES OF PGSP(2) 205 I. PRELIMINARIES 207 1. INTRODUCTION 207 2. STATEMENT OF RESULTS 209 3. THE ZETA FUNCTION 218 4. THE SHIMURA VARIETY 222 5. DECOMPOSITION OF COHOMOLOGY 223 6. GALOIS REPRESENTATIONS 225 II. AUTOMORPHIC REPRESENTATIONS 227 1. STABILIZATION AND THE TEST FUNCTION 227 2. AUTOMORPHIC REPRESENTATIONS OF PGSP(2) 229 3. LOCAL PACKETS 231 4. MULTIPLICITIES 234 5. SPECTRAL SIDE OF THE STABLE TRACE FORMULA 234 6. PROPER ENDOSCOPIC GROUP 236 III. LOCAL TERMS 238 1. REPRESENTATIONS OF THE DUAL GROUP 238 2. LOCAL TERMS AT P 240 3. THE EIGENVALUES AT P 245 4. TERMS AT P FOR THE ENDOSCOPIC GROUP 247 IV. REAL REPRESENTATIONS 248 1. REPRESENTATIONS OF SL(2,R) 248 2. COHOMOLOGICAL REPRESENTATIONS 249 CONTENTS XI 3. NONTEMPERED REPRESENTATIONS 251 4. THE COHOMOLOGICAL L(VSGN, I'- 1/2 7R 2 FC) 252 5. THE COHOMOLOGICAL L(^ 1 / 2 7R 2FE+ I,^- 1/2 ) 254 6. FINITE DIMENSIONAL REPRESENTATIONS 255 7. LOCAL TERMS AT OO 256 V. GALOIS REPRESENTATIONS 258 1. TEMPERED CASE 258 2. NONTEMPERED CASE 262 PART 3. BACKGROUND 267 I. ON AUTOMORPHIC FORMS 269 1. CLASS FIELD THEORY 269 2. REDUCTIVE GROUPS 275 3. FUNCTORIALITY 280 4. UNRAMIFIED CASE 285 5. AUTOMORPHIC REPRESENTATIONS 288 6. RESIDUAL CASE 290 7. ENDOSCOPY 295 8. BASECHANGE 300 II. ON ARTIN'S CONJECTURE 303 REFERENCES 311 INDEX 321
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spelling	Flicker, Yuval Z. Verfasser aut Automorphic forms and shimura varieties of PGSp(2) by Yuval Z FLicker New Jersey [u.a.] World Scientific 2005 XI, 324 S. txt rdacontent n rdamedia nc rdacarrier Formes automorphes Formes automorphes ram Shimura, Variétés de Shimura, Variétés de ram Automorphic forms Shimura varieties Projektive Gruppe (DE-588)4175885-7 gnd rswk-swf Shimura-Mannigfaltigkeit (DE-588)4181143-4 gnd rswk-swf Automorphe Form (DE-588)4003972-9 gnd rswk-swf Symplektische Gruppe (DE-588)4276585-7 gnd rswk-swf Automorphe Form (DE-588)4003972-9 s DE-604 Shimura-Mannigfaltigkeit (DE-588)4181143-4 s Symplektische Gruppe (DE-588)4276585-7 s Projektive Gruppe (DE-588)4175885-7 s GBV Datenaustausch https://bvbr.bib-bvb.de:443/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015466081&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Flicker, Yuval Z. Automorphic forms and shimura varieties of PGSp(2) Formes automorphes Formes automorphes ram Shimura, Variétés de Shimura, Variétés de ram Automorphic forms Shimura varieties Projektive Gruppe (DE-588)4175885-7 gnd Shimura-Mannigfaltigkeit (DE-588)4181143-4 gnd Automorphe Form (DE-588)4003972-9 gnd Symplektische Gruppe (DE-588)4276585-7 gnd
subject_GND	(DE-588)4175885-7 (DE-588)4181143-4 (DE-588)4003972-9 (DE-588)4276585-7
title	Automorphic forms and shimura varieties of PGSp(2)
title_auth	Automorphic forms and shimura varieties of PGSp(2)
title_exact_search	Automorphic forms and shimura varieties of PGSp(2)
title_exact_search_txtP	Automorphic forms and shimura varieties of PGSp(2)
title_full	Automorphic forms and shimura varieties of PGSp(2) by Yuval Z FLicker
title_fullStr	Automorphic forms and shimura varieties of PGSp(2) by Yuval Z FLicker
title_full_unstemmed	Automorphic forms and shimura varieties of PGSp(2) by Yuval Z FLicker
title_short	Automorphic forms and shimura varieties of PGSp(2)
title_sort	automorphic forms and shimura varieties of pgsp 2
topic	Formes automorphes Formes automorphes ram Shimura, Variétés de Shimura, Variétés de ram Automorphic forms Shimura varieties Projektive Gruppe (DE-588)4175885-7 gnd Shimura-Mannigfaltigkeit (DE-588)4181143-4 gnd Automorphe Form (DE-588)4003972-9 gnd Symplektische Gruppe (DE-588)4276585-7 gnd
topic_facet	Formes automorphes Shimura, Variétés de Automorphic forms Shimura varieties Projektive Gruppe Shimura-Mannigfaltigkeit Automorphe Form Symplektische Gruppe
url	https://bvbr.bib-bvb.de:443/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015466081&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT flickeryuvalz automorphicformsandshimuravarietiesofpgsp2

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