CNRS Poncelet

Conference "Zeta Functions"

November 19 - 23, 2012

Moscow, Russia

RAS Poncelet

Organisers: Marc Hindry (Institut de Mathématiques de Jussieu) 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)

Generalizations of Deuring reduction theorem

Alexey Zaytsev (Kaliningrad)

Wednesday November 21, 11:45 - 12:45

Video: [mp4]

Abstract

In the talk we generalize the Deuring theorem on a reduction of elliptic curve with complex multiplication. More precisely, for an Abelian variety $A$, arising after reduction of an Abelian variety with complex multiplication by a CM field $K$ over a number field at a pace of good reduction. We establish a connection between a decomposition of the first truncated Barsotti-Tate group scheme $A[p]$ and a decomposition of $p\cO_{K}$ into prime ideals. In particular, we produce these explicit relationships for Abelian varieties of dimensions $1, 2$ and 3.

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