Arithmétique p-adique des formes de Hilbert:
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| Format: | Book |
| Language: | French |
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Paris
Société mathématique de France
[2016]
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| Series: | Astérisque
382 |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Zusammenfassung in englischer und französischer Sprache |
| Physical Description: | xxii, 266 Seiten |
| ISBN: | 9782856298435 |
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Record in the Search Index
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| adam_text | Titel: Arithmétique p-adique des formes de Hilbert
Autor: Andreatta, Fabrizio
Jahr: 2016
/ARITHMÉTIQUE p-ADIQUE DES FORMES DE HILBERT Fabrizio ANDREATTA, Stéphane BIJAKOWSKI, Adrian IOVITA, Payman L. KASSAEI, Vincent PILLONI, Benoît STROH, Yichao TIAN Liang XIAO
TABLE DES MATIÈRES Introduction ................................................................ xvii Payman L. Kassaei — Analytic Continuation of Overconvergent Hilbert Modular Forms .......................................................... 1 1. The classical case ..................................................... 1 1.1................................................................... 1 1.2. The proof of Coleman’s theorem via analytic continuation ....... 2 1.3. Discussion : the essential ingredients in the second step of analytic continuation .......................................................... 11 2. Hilbert Modular Varieties ............................................. 13 2.1. Notation ......................................................... 13 2.2. The (ip, pj-invariant on Y ........................................ 15 2.3. The type invariant on X ......................................... 16 2.4. The relationship between the type and the ( p,r )) invariants ...... 16 2.5. Definition of the strata ........................................... 17 2.6. The infinitesimal nature of Y .................................... 17 2.7. The geometry of Y ............................................... 20 2.8. The Key Lemma ................................................. 23 2.9. The p-adic geometry of Y ........................................ 24 2.10. The Key Lemma revisited ....................................... 27 3. Domains of automatic analytic continuation .......................... 28 3.1. The preliminaries ................................................ 28 3.2. A guide to visualizing the geometry of f?) r ig ...................... 28 3.3. Analytic continuation, the first step .............................. 29 3.4. Analytic continuation, the second step ........................... 30 4. The Strong Artin Conjecture ......................................... 34 5. Classicality
........................................................... 38 5.1................................................................... 38 5.2. The norm estimates .............................................. 45 References ............................................................... 47 @ Astérisque 382, SMF 2016
TABLE DES MATIÈRES Stéphane Bijakowski — Classicité de formes modulaires de Hilbert ..... Introduction ............................................................. 1. Variété et formes de Hilbert .......................................... 1.1. L’espace de modules .............................................. 1.2. Formes modulaires de Hilbert .................................... 1.3. Normes ........................................................... 2. Opérateurs de Hecke .................................................. 2.1. Définition ........................................................ 2.2. Propriétés ........................................................ 2.3. Décomposition des opérateurs de Hecke .......................... 2.4. Normes ........................................................... 3. Classicité de formes surconvergentes .................................. 3.1. Prolongement automatique ....................................... 3.2. Séries de Kassaei ................................................. 3.3. Fin de la démonstration .......................................... 4. Compactifications et principe de Koecher ............................. 4.1. Compactification toroïdales ...................................... 4.2. Principe de Koecher .............................................. Références ............................................................... Yichao Tian Liang Xiao — p-adic cohomology and classicality of overconvergent Hilbert modular forms ................................... 1. Introduction .......................................................... Structure of the paper ................................................ Acknowledgements .................................................... Notation .............................................................. 2. Preliminaries on Hilbert Modular Varieties and Hilbert Modular Forms 2.1. Shimura varieties for
GL 2 ,f ...................................... 2.2. Automorphic Bundles ............................................ 2.3. Moduli interpretation and integral models ........................ 2.9. Tame Hecke actions on Sh/^ (G) .................................. 2.10. Compactifications ............................................... 2.11. De Rharn cohomology ........................................... 2.12. Integral models of automorphic bundles ......................... 2.14. De Rham complex and Hodge filtrations ........................ 2.15. The dual BGG-complex ......................................... 3. Overconvergent Hilbert Modular Forms ............................... 3.1. Notation ......................................................... 3.2. Hasse invariant and ordinary locus ............................... 3.3. Overconvergent Cusp Forms ...................................... 3.4. Rigid cohomology of the ordinary locus........................... 3.7. Prime-to-p Hecke actions ......................................... 3.10. The operator S p ................................................ 49 49 50 50 53 54 54 54 56 59 60 62 62 62 66 66 66 70 71 73 73 77 78 78 79 79 80 81 85 86 87 88 90 90 92 92 93 93 94 96 98 ASTÉRISQUE 382
TABLE DES MATIÈRES ix 3.11. The p-canonical subgroup ....................................... 99 3.12. Partial Frobenius Pr p ........................................... 100 3.13. Study of p p over the ordinary locus ............................. 101 3.15. C/p-correspondence .............................................. 103 3.18. C/p-operator ..................................................... 105 3.21. Norms .......................................................... 107 4. Formalism of Rigid Cohomology ...................................... 109 4.1. A brief recall of rigid cohomology ................................ 109 4.2. Formalism of dual Cech complex ................................. Ill 4.4. Setup of Hilbert modular varieties ................................ 112 4.5. Isocrystals on the Hilbert modular varieties ...................... 112 4.6. Partial Frobenius on A ........................................... 113 4.9. Twisted partial Frobenius ........................................ 115 4.12. Étale Cohomology .............................................. 118 5. Quaternionic Shimura Varieties and Goren-Oort Stratification ........ 122 5.1. Quaternionic Shimura variety .................................... 122 5.4. Auxiliary CM extension .......................................... 124 5.5. Auxiliary Shimura varieties ...................................... 125 5.6. Automorphic sheaves on Shimura varieties ....................... 126 5.8. Family of Abelian varieties ....................................... 127 5.9. Tensorial induced representations ................................ 128 5.10. Automorphic representations of GL 2 ,f .......................... 129 5.11. Cohomology of Sh J f ( : s (Gs) ....................................... 130 5.13. Cohomology of Sh/c E p (Tb s) .................................... 130 5.21. Description of the GO-stratification of Sh^ p {G !z)f ........... 136 6. Computation of
the Rigid Cohomology I .............................. 140 6.4. Overconvergent Eigenforms of level 70(91) ....................... 146 7. Computation of the Rigid Cohomology II ............................. 150 7.4. Reduction of the proof of Theorem 7.1 ........................... 151 7.5. Contribution of the one-dimensional representations ............. 152 7.6. Contribution of the cuspidal representations ..................... 153 7.7. Cyclic words ..................................................... 154 References ............................................................... 159 Fabrizio Andreatta Adrian Iovita Vincent Pilloni — On overconvergent Hilbert modular cusp forms .............................. 163 1. Introduction .......................................................... 163 2. The weight spaces .................................................... 169 3. Overconvergent modular forms for the group G* ...................... 170 3.1. Hilbert modular varieties ......................................... 170 3.2. The canonical subgroup theory ................................... 171 3.3. The sheaf £7 ...................................................... 173 3.4. The modular sheaves ............................................. 174 SOCIÉTÉ MATHÉMATIQUE DE FRANCE 2016
TABLE DES MATIÈRES 3.5. Families of modular sheaves ...................................... 3.6. The specialization map for cusp forms ........................... 3.7. Hecke operators .................................................. 4. Overconvergent modular forms for the group G ....................... 4.1. Overconvergent descent from G* to G ............................ 4.2. Arithmetic Hilbert modular forms ................................ 4.3. Hecke operators .................................................. 5. The arithmetic eigenvariety ........................................... 6. An appendix : Some toric geometry ................................... References ............................................................... Vincent Pilloni Benoît Stroh — Surconvergence, ramification et modularité ............................................................... Partie I. Réductions et preuve des corollaires ............................ 1. Une forme faible du théorème ......................................... 2. Modularité résiduelle ................................................. 2.1. Modularité potentielle des représentations icosahédrales .......... 2.2. Corollaires ....................................................... Partie II. Déformations et méthode de Taylor-Wiles-Kisin ............... 3. L’algèbre A et les déformations du déterminant ....................... 4. Anneaux de déformations locales ..................................... 4.1. En les places divisant p .......................................... 4.2. En les places de Taylor-Wiles .................................... 4.3. Représentations spéciales ......................................... 5. Anneaux de déformations globales .................................... 5.1. Notations et définitions .......................................... 5.2. Calculs d’espaces tangents ....................................... 6. Variétés
de Hilbert .................................................... 6.1. Variétés abéliennes de Hilbert polarisées ......................... 6.2. Le faisceau des formes modulaires ................................ 6.3. Action du centre ................................................. 6.4. Ajout de niveau en les places de Taylor-Wiles .................... 6.5. Algèbres de Hecke ................................................ 6.6. Théorie de Hida .................................................. 6.7. Les modules ...................................................... 7. La méthode de Taylor-Wiles-Kisin .................................... 7.1. Représentations galoisiennes ...................................... 7.2. Un théorème de relèvement modulaire ............................ Partie III. Classicité de formes modulaires surconvergentes .............. 8. Enoncé du critère de classicité ........................................ 9. Préliminaires sur les schémas en groupes .............................. 176 178 182 184 184 188 188 189 190 192 195 200 200 202 202 203 204 205 205 205 210 210 211 211 212 213 213 214 214 217 218 219 219 221 221 222 227 227 228 ASTÉRISQUE 382
TABLE DES MATIÈRES xi 9.1. Groupes de Hilbert-Blumenthal Barsotti-Tate .................... 228 9.2. Généralités sur les BTHB en caractéristique p .................... 229 9.3. Déformations de BTHB .......................................... 236 9.4. Théorie du modèle local .......................................... 239 9.5. Rigidité de certains BTHB non simples .......................... 245 10. Classicité ............................................................ 251 10.1. Une stratification ............................................... 251 10.2. Dynamique des opérateurs de Hecke ............................ 253 10.3. Première étape du prolongement ................................ 256 10.4. Le mauvais lieu ................................................. 257 10.5. Prolongement sur Zoo (p,*) ...................................... 257 10.6. Fin de la preuve ................................................. 263 Références ............................................................... 264 SOCIÉTÉ MATHÉMATIQUE DE FRANCE 2016
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| author | Andreatta, Fabrizio 1972- Bijakowski, Stéphane Ioviţă, Adrian Kassaei, Payman L. 1973- Pilloni, Vincent Stroh, Benoît Tian, Yichao Xiao, Liang |
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| author_facet | Andreatta, Fabrizio 1972- Bijakowski, Stéphane Ioviţă, Adrian Kassaei, Payman L. 1973- Pilloni, Vincent Stroh, Benoît Tian, Yichao Xiao, Liang |
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| spelling | Andreatta, Fabrizio 1972- (DE-588)173744788 aut Arithmétique p-adique des formes de Hilbert Fabrizio Andreatta, Stéphane Bijakowski, Adrian Iovita, Payman L. Kassaei, Vincent Pilloni, Benoît Stroh, Yichao Tian & Liang Xiao Paris Société mathématique de France [2016] © 2016 xxii, 266 Seiten txt rdacontent n rdamedia nc rdacarrier Astérisque 382 Zusammenfassung in englischer und französischer Sprache Bijakowski, Stéphane aut Ioviţă, Adrian aut Kassaei, Payman L. 1973- (DE-588)1100354603 aut Pilloni, Vincent aut Stroh, Benoît aut Tian, Yichao aut Xiao, Liang (DE-588)1129608506 aut Astérisque 382 (DE-604)BV002579439 382 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029316109&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Andreatta, Fabrizio 1972- Bijakowski, Stéphane Ioviţă, Adrian Kassaei, Payman L. 1973- Pilloni, Vincent Stroh, Benoît Tian, Yichao Xiao, Liang Arithmétique p-adique des formes de Hilbert Astérisque |
| title | Arithmétique p-adique des formes de Hilbert |
| title_auth | Arithmétique p-adique des formes de Hilbert |
| title_exact_search | Arithmétique p-adique des formes de Hilbert |
| title_full | Arithmétique p-adique des formes de Hilbert Fabrizio Andreatta, Stéphane Bijakowski, Adrian Iovita, Payman L. Kassaei, Vincent Pilloni, Benoît Stroh, Yichao Tian & Liang Xiao |
| title_fullStr | Arithmétique p-adique des formes de Hilbert Fabrizio Andreatta, Stéphane Bijakowski, Adrian Iovita, Payman L. Kassaei, Vincent Pilloni, Benoît Stroh, Yichao Tian & Liang Xiao |
| title_full_unstemmed | Arithmétique p-adique des formes de Hilbert Fabrizio Andreatta, Stéphane Bijakowski, Adrian Iovita, Payman L. Kassaei, Vincent Pilloni, Benoît Stroh, Yichao Tian & Liang Xiao |
| title_short | Arithmétique p-adique des formes de Hilbert |
| title_sort | arithmetique p adique des formes de hilbert |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029316109&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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