Abstract

In this talk, I will explain a joint work with Xu Shen on geometry of good reductions of Shimura varieties of abelian type. More precisely, we construct the Newton stratication, Ekedahl-Oort stratication, and central leaves on the special ber of a Shimura variety of abelian type at a good prime. We establish basic properties of these stratications, including the non-emptiness, closure relation and dimension formula, generalizing those previously known in the PEL and Hodge type cases. We also study the relations between these stratications, both in general and in some special cases, such as those of fully Hodge-Newton decomposable type. I will explain our results applied to quaternionic and orthogonal Shimura varieties if time permits.