G-zips and Ekedahl-Oort strata for Hodge type Shimura varieties

Abstract

We constructed a G-zip over the special fiber of Kisin's integral canonical model. This induces a morphism from the special fiber to the stack of G-zips. Fibers of this morphism are Ekedahl-Oort strata. We proved that this morphism is smooth, and hence we can transfer results about geometry of the stack of G-zips to results about Ekedahl-Oort strata. In particular, each stratum is smooth, and we know its dimension and closure.