The \mu-ordinary locus for Shimura varieties of Hodge type

TL;DR

This paper studies the -ordinary locus in Shimura varieties of Hodge type, showing it is dense and coincides with the generic Ekedahl-Oort stratum, extending known results beyond PEL cases.

Contribution

It establishes the density and characterization of the -ordinary locus for Hodge type Shimura varieties, generalizing previous PEL case results and introducing a group-theoretic reduction method.

Findings

-ordinary locus is open and dense

It coincides with the generic Ekedahl-Oort stratum

Provides a group-theoretic method for stratification analysis

Abstract

We review the Newton stratification and Ekedahl-Oort stratification on the special fiber of a smooth integral model for a Shimura variety of Hodge type at a prime of good reduction. We show that the \mu-ordinary locus coincides with the generic Ekedahl-Oort stratum, and that for any two geometric points in the \mu-ordinary locus there is an isomorphism of the attached Dieudonne modules with additional structure. As a consequence, we proof that the \mu-ordinary locus is open and dense, thus generalizing the results which were already known in the PEL-case. To prove our results we provide a method which allows to reduce the equality of strata to a group theoretic statement.