Conference "Global Fields"
October 25 - 28, 2011
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)
Tuesday 25 October, 17:00 - 18:30
Let A be an abelian variety over a number field L with complex multiplication by the full ring of integers O_K for some CM field K. If A has a good reduction at a prime ideal S in L then A mod S is an abelian variety over a finite field of characteristic p. In this talk, we will study a correspondence between the decomposition of ideal pO_K into prime ideals (unramified case) and decomposition of the first truncated Barsotti-Tate group scheme (A mod S)[p]. We will try to undestand p-torsion points of the abelian variety (A mod S) (as a group scheme, i.e. in functorial sence) from two points of views, algebraic number theory and arithmetic geometry. In addition, I will discuss a moduli problem of abelian varieties up to isogeny.