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arXiv · 2606.16882

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

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

In this paper, we give a complete classification of indecomposable Ekedahl--Oort strata of Shimura varieties associated to the unitary group $\mathsf{GU}(a, b)$ over an odd inert prime. We show that each indecomposable stratum is one of four types: unitary unicycle, unitary bicycle, Serre unicycle, or Serre bicycle; the latter two types are named for a tensor construction of abelian varieties developed by Serre. We provide an algorithm that translates the description of a stratum in terms of words in the alphabet $\{\texttt{f},\texttt{v}\}$ to the corresponding Weyl group coset representative. Finally, using a $p$-adic lift, we construct a `tautological' point in each Ekedahl--Oort stratum, and compute its Newton polygon. As an application, we show that the indecomposable Ekedahl--Oort strata corresponding to unitary unicycles and Serre unicycles always intersect the supersingular locus.

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Emerald Andrews, Deewang Bhamidipati, Maria Fox, Heidi Goodson, Steven R. Groen, Sandra Nair. 2026-06-15. On the classification of indecomposable Ekedahl-Oort strata in unitary Shimura varieties, and related Newton polygons. https://arxiv.org/abs/2606.16882

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