Around the Zilber-Pink conjecture: = Autour de la conjecture de Zilber-Pink
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| Main Authors: | , , , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Marseille
Société Mathématique de France
2017
|
| Series: | Panoramas et synthèses
52 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Textes en anglais et en français, résumés en anglais |
| Physical Description: | XIV, 284 Seiten Illustrationen 24 cm |
| ISBN: | 9782856298565 2856298567 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804178235167080448 |
|---|---|
| adam_text | TABLE DES MATIÈRES
Avant-propos................................................................ xi
Foreword.................................................................. xiii
Emmanuel Ullmo — Structures spéciales et problème de Zilber-Pink.......... 1
1. Introduction............................................................. 1
2. Une version abstraite de la conjecture de Zilber-Pink.................... 2
3. La conjecture de Zilber-Pink............................................ 20
Références.............................................................. 26
Emmanuel Ullmo — Autour de la conjecture d’André-Oort................. 31
1. Introduction............................................................ 31
2. La conjecture d’André-Oort pour un produit de courbes modulaires...... 32
3. Variétés de Shimura..................................................... 50
4. Théorie ergodique sur les espaces homogènes............................. 74
5. Equidistribution des sous-variétés spéciales des variétés de Shimura.. 81
Références.............................................................. 85
Andrei Yafaev — Special points and intersections in Abelian and Shimura
varieties............................................................... 89
1. Introduction............................................................ 89
Acknowledgements........................................................ 90
2. Preliminaries on Equidistribution....................................... 91
3. Strategy of the proof................................................... 93
4. The Manin-Mumford conjecture via Galois orbits and Equidistribution . . 93
5. Shimura case : lower bounds for Galois orbits and the alternative..... 99
6. The geometric criterion and the end of the proof....................... 104
7. Choice of a suitable Hecke correspondence ............................. 107
8. End of the proof : the induction....................................... 107
References............................................................. 109
Thomas Scanlon — O-minimality as an approach to the André-Oort conjecture 111
1. Introduction........................................................... Ill
2. Overview of the Pila-Zannier strategy.................................. 112
VI
TABLE DES MATIÈRES
3. O-minimality............................................................ 116
4. Pila-Wilkie counting theorem............................................ 129
5. Applications of the counting theorem to diophantine geometry............ 145
References.............................................................. 161
Philipp Habegger — Effective Height Upper Bounds on Algebraic Tori ... . 167
0. Introduction............................................................ 167
1. A Brief Historical Overview in the Toric Setting........................ 168
2. An Effective Height Bound............................................... 173
3. Notation................................................................ 176
4. Estimates for Hilbert Functions......................................... 182
5. More on Segre and Veronese.............................................. 188
6. Correspondences and Height Inequalities................................. 194
7. Degree and Height Upper Bounds for Compactifications ................... 215
8. Tropical Geometry and Degree Lower Bounds............................... 219
9. Generically Bounded Height.............................................. 227
10. Bounded Height .......................................................... 232
A. The Case of Abelian Varieties........................................... 235
B. Height Bounds in Shimura Varieties...................................... 237
References.............................................................. 239
Gaël Rémond — Généralisations du problème de Lehmer et applications à la
conjecture de Zilber-Pink............................................... 243
1. Introduction............................................................ 243
2. Hauteur................................................................. 245
3. Minorations de hauteurs normalisées .................................... 251
4. Liens avec la conjecture de Zilber-Pink ................................ 265
5. Variétés semi-abéliennes................................................ 276
6. Appendice : projecteurs normalisés...................................... 278
7. Développements récents.................................................. 281
Références.............................................................. 281
PANORAMAS SYNTHÈSES 52
|
| any_adam_object | 1 |
| author | Habegger, Philipp 1978- Rémond, Gaël Scanlon, Thomas Ullmo, Emmanuel Yafaev, A. |
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| author_role | aut aut aut aut aut |
| author_sort | Habegger, Philipp 1978- |
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| building | Verbundindex |
| bvnumber | BV044735722 |
| classification_rvk | SK 180 SK 240 |
| ctrlnum | (OCoLC)1027750266 (DE-599)BVBBV044735722 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV044735722 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T08:00:45Z |
| institution | BVB |
| isbn | 9782856298565 2856298567 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030131695 |
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| physical | XIV, 284 Seiten Illustrationen 24 cm |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | Société Mathématique de France |
| record_format | marc |
| series | Panoramas et synthèses |
| series2 | Panoramas et synthèses |
| spelling | Habegger, Philipp 1978- Verfasser (DE-588)1123243166 aut Around the Zilber-Pink conjecture = Autour de la conjecture de Zilber-Pink P. Habegger, G. Rémond, T. Scanlon, E. Ullmo, A. Yafaev Autour de la conjecture de Zilber-Pink Marseille Société Mathématique de France 2017 XIV, 284 Seiten Illustrationen 24 cm txt rdacontent n isbdmedia rdamedia nc rdacarrier Panoramas et synthèses 52 Textes en anglais et en français, résumés en anglais Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Arithmetische Geometrie (DE-588)4131383-5 gnd rswk-swf Géométrie algébrique arithmétique (DE-588)4143413-4 Aufsatzsammlung gnd-content Algebraische Geometrie (DE-588)4001161-6 s Arithmetische Geometrie (DE-588)4131383-5 s DE-604 Rémond, Gaël aut Scanlon, Thomas (DE-588)1153504480 aut Ullmo, Emmanuel (DE-588)1103599038 aut Yafaev, A. (DE-588)1103599410 aut Panoramas et synthèses 52 (DE-604)BV037491878 52 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030131695&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Habegger, Philipp 1978- Rémond, Gaël Scanlon, Thomas Ullmo, Emmanuel Yafaev, A. Around the Zilber-Pink conjecture = Autour de la conjecture de Zilber-Pink Panoramas et synthèses Algebraische Geometrie (DE-588)4001161-6 gnd Arithmetische Geometrie (DE-588)4131383-5 gnd |
| subject_GND | (DE-588)4001161-6 (DE-588)4131383-5 (DE-588)4143413-4 |
| title | Around the Zilber-Pink conjecture = Autour de la conjecture de Zilber-Pink |
| title_alt | Autour de la conjecture de Zilber-Pink |
| title_auth | Around the Zilber-Pink conjecture = Autour de la conjecture de Zilber-Pink |
| title_exact_search | Around the Zilber-Pink conjecture = Autour de la conjecture de Zilber-Pink |
| title_full | Around the Zilber-Pink conjecture = Autour de la conjecture de Zilber-Pink P. Habegger, G. Rémond, T. Scanlon, E. Ullmo, A. Yafaev |
| title_fullStr | Around the Zilber-Pink conjecture = Autour de la conjecture de Zilber-Pink P. Habegger, G. Rémond, T. Scanlon, E. Ullmo, A. Yafaev |
| title_full_unstemmed | Around the Zilber-Pink conjecture = Autour de la conjecture de Zilber-Pink P. Habegger, G. Rémond, T. Scanlon, E. Ullmo, A. Yafaev |
| title_short | Around the Zilber-Pink conjecture |
| title_sort | around the zilber pink conjecture autour de la conjecture de zilber pink |
| title_sub | = Autour de la conjecture de Zilber-Pink |
| topic | Algebraische Geometrie (DE-588)4001161-6 gnd Arithmetische Geometrie (DE-588)4131383-5 gnd |
| topic_facet | Algebraische Geometrie Arithmetische Geometrie Aufsatzsammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030131695&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV037491878 |
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