Newton polygon strata in the moduli space of abelian varieties

Abstract

We consider p-divisible groups (also called Barsotti-Tate groups) in characteristic p, abelian varieties, their deformations, and we draw some conclusions. For a p-divisible group in characteristic p, we can define its Newton polygon. This is invariant under isogeny. For an abelian variety the Newton Polygon of its p-divisible group is symmetric. We are interested in the strata defined by Newton Polygons in local deformation spaces or in the moduli space of polarized abelian varieties