This paper describes the interaction of Ekedahl-Oort and Newton stratifications in GU(3,2) Shimura varieties, revealing intersection properties among their strata.
This paper concerns the characteristic-p fibers of GU(3,2) Shimura varieties. Such Shimura varieties parametrize abelian varieties in characteristic p of dimension $5$ with an action of signature $(3,2)$ by an order in an imaginary quadratic field in which p is inert. We completely describe the interaction of two stratifications of these Shimura varieties: 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. We identify which Ekedahl-Oort and Newton strata intersect.
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Andrews et al. (2025) studied this question.
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