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

Emerald Andrews, Deewang Bhamidipati, Maria Fox, Heidi Goodson, Steven R. Groen, Sandra Nair

Published: 2024/5/7

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 $(q-2,2)$.

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