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June 20, 2026Open Access

On the classification of indecomposable Ekedahl-Oort strata in unitary Shimura varieties, and related Newton polygons

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The aim is to classify indecomposable Ekedahl-Oort strata in unitary Shimura varieties associated with the unitary group GU(a, b).
Classified each indecomposable stratum into four types: unitary unicycle, unitary bicycle, Serre unicycle, and Serre bicycle.
Developed an algorithm to translate descriptions of strata into Weyl group coset representatives.
Constructed a p-adic lift to form a 'tautological' point in each Ekedahl-Oort stratum and computed its Newton polygon.
Identified four types of indecomposable strata, with specific tensor constructions named after Serre.
Demonstrated that indecomposable Ekedahl-Oort strata for unitary unicycles and Serre unicycles intersect the supersingular locus.

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Classifies indecomposable Ekedahl-Oort strata in unitary Shimura varieties, indicating implications for abelian varieties.

Andrews et al. (2026) studied this question.

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