A local construction of zip period maps of Shimura varieties

Abstract

Let $S$ be the special fibre of a Shimura variety of Hodge type of good reduction at a fixed place above $p$. We give a local approach to the construction of the zip period map for $S$, which is used to define the Ekedahl–Oort strata of $S$. The method employed is $p$-adic and group theoretic in nature.