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Conference "Global Fields"October 25 - 28, 2011Moscow, Russia |
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Conference "Global Fields"October 25 - 28, 2011Moscow, Russia |
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Organisers: Philippe Lebacque (Laboratoire de Mathématiques de Besançon ), Michael Tsfasman (CNRS, Laboratoire Poncelet, Institute for Information Transmission Problems), Alexey Zykin (Laboratoire Poncelet, State University Higher School of Economics, IITP)
Wednesday 26 October, 12:00 - 13:30
For an abelian variety defined over a global field, the cardinality of its Tate-Shafarevic group (known or conjectured to be finite...) and the Neron-Tate regulator are among its most important invariant. We'll discuss the question wether the product of those two quantities is asymptotically similar to the (exponential) height of the abelian variety. We will specially discuss the case of the family of twists of a given abelian variety.
This is joint work and work in progress with Amilcar Pacheco.