p-adic automorphic forms on Shimura varieties:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2004
|
| Schriftenreihe: | Springer monographs in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XI, 390 S. |
| ISBN: | 0387207112 9780387207117 |
Internformat
MARC
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| 100 | 1 | |a Hida, Haruzo |d 1952- |e Verfasser |0 (DE-588)129238260 |4 aut | |
| 245 | 1 | 0 | |a p-adic automorphic forms on Shimura varieties |c Haruzo Hida |
| 264 | 1 | |a New York [u.a.] |b Springer |c 2004 | |
| 300 | |a XI, 390 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer monographs in mathematics | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Analyse p-adique | |
| 650 | 4 | |a Formes automorphes | |
| 650 | 7 | |a P-adische getallen |2 gtt | |
| 650 | 7 | |a Shimura variëteiten |2 gtt | |
| 650 | 4 | |a Shimura, Variétés de | |
| 650 | 4 | |a Automorphic forms | |
| 650 | 4 | |a Shimura varieties | |
| 650 | 4 | |a p-adic analysis | |
| 650 | 0 | 7 | |a Automorphe Form |0 (DE-588)4003972-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a p-adische Analysis |0 (DE-588)4252360-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Shimura-Mannigfaltigkeit |0 (DE-588)4181143-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Shimura-Mannigfaltigkeit |0 (DE-588)4181143-4 |D s |
| 689 | 0 | 1 | |a Automorphe Form |0 (DE-588)4003972-9 |D s |
| 689 | 0 | 2 | |a p-adische Analysis |0 (DE-588)4252360-6 |D s |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-012825875 | ||
Datensatz im Suchindex
| _version_ | 1804132796938059776 |
|---|---|
| adam_text | Contents
1 Introduction 1
1.1 Automorphic Forms on Classical Groups 5
1.2 p Adic Interpolation of Automorphic Forms 8
1.3 p Adic Automorphic L functions 12
1.4 Galois Representations 13
1.5 Plan of the Book 13
1.6 Notation 15
2 Geometrie Reciprocity Laws 17
2.1 Sketch of Classical Reciprocity Laws 18
2.1.1 Quadratic Reciprocity Law 18
2.1.2 Cyclotomic Version 19
2.1.3 Geometrie Interpretation 20
2.1.4 Kronecker s Reciprocity Law 21
2.1.5 Reciprocity Law for Elliptic Curves 24
2.2 Cyclotomic Reciprocity Laws and Adeles 24
2.2.1 Cyclotomic Fields 24
2.2.2 Cyclotomic Reciprocity Laws 26
2.2.3 Adelic Reformulation 28
2.3 A Generalization of Galois Theory 31
2.3.1 Infinite Galois Extensions 31
2.3.2 Automorphism Group of a Field 35
2.4 Algebraic Curves over a Field 36
2.4.1 Algebraic Function Fields 36
2.4.2 Zariski Topology 43
2.4.3 Divisors 44
2.4.4 Differentials 45
2.4.5 Adele Rings of Algebraic Function Fields 50
2.5 Elliptic Curves over a Field 51
2.5.1 Dimension Formulas 51
2.5.2 Weierstrass Equations of Elliptic Curves 52
2.5.3 Moduli of Weierstrass Type 54
2.5.4 Group Structure on Elliptic Curves 55
2.5.5 Abel s Theorem 56
2.5.6 Torsion Points on Elliptic Curves 57
2.5.7 Classical Weierstrass Theory 60
2.6 Elliptic Modular Function Field 62
3 Modular Curves 67
3.1 Basics of Elliptic Curves over a Scheine 67
3.1.1 Definition of Elliptic Curves 68
3.1.2 Cartier Divisors 68
3.1.3 Picard Scheines 69
3.1.4 Invariant Differentials 70
3.1.5 Classification Functors 70
3.1.6 Cartier Duality 71
3.2 Moduli of Elliptic Curves and the Igusa Tower 72
3.2.1 Moduli of Level 1 over 1[ 72
3.2.2 Moduli of Vri(N) 74
3.2.3 Action of Gm 75
3.2.4 Compactification 77
3.2.5 Moduli of r(A0 Level Structure 79
3.2.6 Hasse Invariant 80
3.2.7 Igusa Curves 81
3.2.8 Irreducibility of Igusa Curves 82
3.2.9 p Adic Elliptic Modular Forms 85
3.3 p Ordinary Elliptic Modular Forms 86
3.3.1 Axiomatic Treatment 86
3.3.2 Bounding the p Ordinary Rank 89
3.3.3 p Ordinary Projector 90
3.3.4 Families of p Ordinary Modular Forms 90
3.4 Elliptic vl Adic Forms and p Adic L functions 92
3.4.1 Generality of yl Adic Forms 92
3.4.2 Some p Adic L Functions 94
4 Hubert Modular Varieties 97
4.1 Hilbert Blumenthal Moduli 98
4.1.1 Abelian Variety with Real Multiplication 98
4.1.2 Moduli Problems with Level Structure 102
4.1.3 Complex Analytic Hubert Modular Forms 104
4.1.4 Toroidal Compactification 110
4.1.5 Täte Semi Abelian Scheines with Real Multiplication . . 115
4.1.6 Hasse Invariant and Sheaves of Cusp Forms 117
4.1.7 p Adic Hubert Modular Forms of Level r(N) 119
4.1.8 Moduli Problem of T/(9t) Type 123
4.1.9 p Adic Modular Forms on PGL(2) 125
4.1.10 Hecke Operators on Geometrie Modular Forms 127
4.2 Hubert Modular Shimura Varieties 131
4.2.1 Abelian Varieties up to Isogenies 133
4.2.2 Global Reciprocity Law 140
4.2.3 Local Reciprocity Law 154
4.2.4 Hubert Modular Igusa Towers 158
4.2.5 Hecke Operators as Algebraic Correspondences 164
4.2.6 Modular Line Bundles 165
4.2.7 Sheaves over the Shimura Variety of PGL(2) 175
4.2.8 Hecke Algebra of Finite Level 177
4.2.9 Effect on q Expansion 178
4.2.10 Adelic q Expansion 184
4.2.11 Nearly Ordinary Hecke Algebra with Central Character 189
4.2.12 p Adic Universal Hecke Algebra 191
4.3 Rank of p Ordinary Cohomology Groups 192
4.3.1 Archimedean Automorphic Forms 192
4.3.2 Jacquet Langlands Shimizu Correspondence 198
4.3.3 Integral Correspondence 202
4.3.4 Eichler Shimura Isomorphisms 205
4.3.5 Constant Dimensionality 206
4.4 Appendix: Fundamental Groups 209
4.4.1 Categorical Galois Theory 209
4.4.2 Algebraic Fundamental Groups 216
4.4.3 Group Theoretic Results 218
5 Generalized Eichler Shimura Map 225
5.1 Semi Simplicity of Hecke Algebras 225
5.1.1 Jacquet Modules 226
5.1.2 Double Coset Algebras 227
5.1.3 Rational Representations of G 230
5.1.4 Nearly p Ordinary Representations 232
5.1.5 Semi Simplicity of Interior Cohomology Groups 234
5.2 Explicit Symmetrie Domains 236
5.2.1 Hermitian Forms over C 236
5.2.2 Symmetrie Spaces of Unitary Groups 238
5.2.3 Invariant Measure 243
5.3 The Eichler Shimura Map 244
5.3.1 Unitary Groups 245
5.3.2 Symplectic Groups 247
5.3.3 Hecke Equivariance 248
6 Moduli Schemes 251
6.1 Hubert Schemes 251
6.1.1 Vector Bundles 252
6.1.2 Grassmannians 253
6.1.3 Flag Varieties 256
6.1.4 Fiat Quotient Modules 258
6.1.5 Morphisms Between Schemes 262
6.1.6 Abelian Schemes 264
6.2 Quotients by PGL(n) 269
6.2.1 Line Bundles on Projective Spaces 270
6.2.2 Automorphism Group of a Projective Space 270
6.2.3 Quotient of a Product of Projective Spaces 271
6.3 Mumford Moduli 276
6.3.1 Dual Abelian Scheme and Polarization 276
6.3.2 Moduli Problem 276
6.3.3 Abelian Scheme with Linear Rigidification 278
6.3.4 Embedding into the Hubert Scheme 279
6.3.5 Conclusion 280
6.3.6 Smooth Toroidal Compactification 282
6.4 Siegel Modular Variety 290
6.4.1 Moduli Functors 291
6.4.2 Siegel Modular Reciprocity Law 293
6.4.3 Siegel Modular Igusa Tower 296
7 Shimura Varieties 303
7.1 PEL Moduli Varieties 304
7.1.1 Polarization, Endomorphism, and Lattice 304
7.1.2 Construction of the Moduli 309
7.1.3 Moduli Variety for Similitude Groups 314
7.1.4 Classification of G 316
7.1.5 Generic Fiber of Sh^} 317
7.2 General Shimura Varieties 321
7.2.1 Axioms Defining Shimura Varieties 321
7.2.2 Reciprocity Law at Special Points 324
7.2.3 Shimura s Reciprocity Law 326
8 Ordinary p Adic Automorphic Forms 329
8.1 True and False Automorphic Forms 329
8.1.1 An Axiomatic Igusa Tower 330
8.1.2 Rational Representation and Vector Bundles 331
8.1.3 Weight of Automorphic Forms and Representations .... 333
8.1.4 Density Theorems 335
8.1.5 p Ordinary Automorphic Forms 339
8.1.6 Construction of the Projector eGz, 341
8.1.7 Axiomatic Control Result 344
8.2 Deformation Theory of Serre and Täte 345
8.2.1 A Theorem of Drinfeld 346
8.2.2 A Theorem of Serre Tate 348
8.2.3 Deformation of an Ordinary Abelian Variety 349
8.2.4 Symplectic Case 350
8.2.5 Unitary Case 351
8.3 Vertical Control Theorem 355
8.3.1 Hecke Operators on Deformation Space 356
8.3.2 Statements and Proof 360
8.4 Irreducibility of Igusa Towers 363
8.4.1 Irreducibility and p Decomposition Groups 364
8.4.2 Closed Immersion into the Siegel Modular Variety 364
8.4.3 Description of a p Decomposition Group 367
8.4.4 Irreducibility Theorem in Cases A and C 369
References 375
Symbol Index 383
Statement Index 385
Subject Index 387
|
| any_adam_object | 1 |
| author | Hida, Haruzo 1952- |
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| dewey-ones | 515 - Analysis |
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| dewey-search | 515/.9 |
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| discipline | Mathematik |
| format | Book |
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| language | English |
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| spelling | Hida, Haruzo 1952- Verfasser (DE-588)129238260 aut p-adic automorphic forms on Shimura varieties Haruzo Hida New York [u.a.] Springer 2004 XI, 390 S. txt rdacontent n rdamedia nc rdacarrier Springer monographs in mathematics Includes bibliographical references and index Analyse p-adique Formes automorphes P-adische getallen gtt Shimura variëteiten gtt Shimura, Variétés de Automorphic forms Shimura varieties p-adic analysis Automorphe Form (DE-588)4003972-9 gnd rswk-swf p-adische Analysis (DE-588)4252360-6 gnd rswk-swf Shimura-Mannigfaltigkeit (DE-588)4181143-4 gnd rswk-swf Shimura-Mannigfaltigkeit (DE-588)4181143-4 s Automorphe Form (DE-588)4003972-9 s p-adische Analysis (DE-588)4252360-6 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012825875&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hida, Haruzo 1952- p-adic automorphic forms on Shimura varieties Analyse p-adique Formes automorphes P-adische getallen gtt Shimura variëteiten gtt Shimura, Variétés de Automorphic forms Shimura varieties p-adic analysis Automorphe Form (DE-588)4003972-9 gnd p-adische Analysis (DE-588)4252360-6 gnd Shimura-Mannigfaltigkeit (DE-588)4181143-4 gnd |
| subject_GND | (DE-588)4003972-9 (DE-588)4252360-6 (DE-588)4181143-4 |
| title | p-adic automorphic forms on Shimura varieties |
| title_auth | p-adic automorphic forms on Shimura varieties |
| title_exact_search | p-adic automorphic forms on Shimura varieties |
| title_full | p-adic automorphic forms on Shimura varieties Haruzo Hida |
| title_fullStr | p-adic automorphic forms on Shimura varieties Haruzo Hida |
| title_full_unstemmed | p-adic automorphic forms on Shimura varieties Haruzo Hida |
| title_short | p-adic automorphic forms on Shimura varieties |
| title_sort | p adic automorphic forms on shimura varieties |
| topic | Analyse p-adique Formes automorphes P-adische getallen gtt Shimura variëteiten gtt Shimura, Variétés de Automorphic forms Shimura varieties p-adic analysis Automorphe Form (DE-588)4003972-9 gnd p-adische Analysis (DE-588)4252360-6 gnd Shimura-Mannigfaltigkeit (DE-588)4181143-4 gnd |
| topic_facet | Analyse p-adique Formes automorphes P-adische getallen Shimura variëteiten Shimura, Variétés de Automorphic forms Shimura varieties p-adic analysis Automorphe Form p-adische Analysis Shimura-Mannigfaltigkeit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012825875&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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