Ekedahl-Oort strata in the $\mathsf{GU}(q-2,2)$ Shimura variety

TL;DR

This paper studies the structure of certain Shimura varieties in characteristic p, focusing on the Ekedahl-Oort stratification and its relation to the Newton stratification, providing new insights and techniques for the case of signature (q-2,2).

Contribution

The paper introduces novel methods to analyze the Ekedahl-Oort stratification and its interaction with Newton stratification for $ ext{GU}(q-2,2)$ Shimura varieties.

Findings

Enhanced understanding of the Ekedahl-Oort stratification.

New techniques for analyzing stratification interactions.

Results applicable to general signature (q-2,2).

Abstract

This paper concerns the characteristic-$p$ fibers of $\mathsf{GU}(q-2,2)$ Shimura varieties, which classify abelian varieties with additional structure. These Shimura varieties admit two stratifications of interest: the Ekedahl-Oort stratification, based on the isomorphism class of the $p$-torsion subgroup scheme, and the Newton stratification, based on the isogeny class of the $p$-divisible group. In this paper, we present several novel techniques that give a better understanding of the Ekedahl-Oort stratification and of the interaction between the two stratifications for a general signature $(q-2,2)$.