Conference "Global Fields"

Abelian varieties with complex multiplication and their first truncated Barsotti-Tate group schemes

Alexey Zaytsev (Kaliningrad)

Tuesday 25 October, 17:00 - 18:30

Abstract

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.