An alternative construction of zip period maps for Shimura varieties

TL;DR

This paper introduces a new local, p-adic, group-theoretic method for constructing the zip period map on the special fiber of Hodge type Shimura varieties, aiding in defining Ekedahl-Oort strata.

Contribution

It provides an alternative, group-theoretic construction of the zip period map, enhancing understanding of the stratification of Shimura varieties in characteristic p.

Findings

New construction of zip period map using local p-adic methods

Facilitates the definition of Ekedahl-Oort strata

Offers a group-theoretic perspective on Shimura variety stratification

Abstract

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