| Softcover ISBN: | 978-2-85629-856-5 |
| Product Code: | PASY/52 |
| List Price: | $82.00 |
| AMS Member Price: | $65.60 |
| Softcover ISBN: | 978-2-85629-856-5 |
| Product Code: | PASY/52 |
| List Price: | $82.00 |
| AMS Member Price: | $65.60 |
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Book DetailsPanoramas et SynthèsesVolume: 52; 2017; 284 ppMSC: Primary 03; 11; 14; 22
Following Faltings and Vojta's work proving the Mordell-Lang conjecture for abelian varieties and Raynaud's work proving the Manin-Mumford conjecture, many new diophantine questions appeared, often described as problems of unlikely intersections. The arithmetic of moduli spaces of abelian varieties and, more generally, Shimura varieties has been parallel-developed around the central André-Oort conjecture. These two themes can be placed in a common frame—the Zilber-Pink conjecture.
This volume is an introduction to these problems and to the various techniques used: geometry, height theory, reductive groups and Hodge theory, Shimura varieties, and model theory via the notion of o-minimal structure. The volume contains texts corresponding to courses presented at CIRM in May 2011 by Philipp Habegger, Gaël Rémond, Thomas Scanlon, Emmanuel Ullmo, and Andrei Yafaev and an ample introduction by E. Ullmo centered on the notion of bi-algebraicity aimed at a presentation of the general setting.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
ReadershipGraduate students and researchers interested in the Zilber-Pink conjecture.
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Following Faltings and Vojta's work proving the Mordell-Lang conjecture for abelian varieties and Raynaud's work proving the Manin-Mumford conjecture, many new diophantine questions appeared, often described as problems of unlikely intersections. The arithmetic of moduli spaces of abelian varieties and, more generally, Shimura varieties has been parallel-developed around the central André-Oort conjecture. These two themes can be placed in a common frame—the Zilber-Pink conjecture.
This volume is an introduction to these problems and to the various techniques used: geometry, height theory, reductive groups and Hodge theory, Shimura varieties, and model theory via the notion of o-minimal structure. The volume contains texts corresponding to courses presented at CIRM in May 2011 by Philipp Habegger, Gaël Rémond, Thomas Scanlon, Emmanuel Ullmo, and Andrei Yafaev and an ample introduction by E. Ullmo centered on the notion of bi-algebraicity aimed at a presentation of the general setting.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
Graduate students and researchers interested in the Zilber-Pink conjecture.
