The Ekedahl-Oort and Newton stratification of the GU(3,2) Shimura variety

2025/10/01 by Andrews, Emerald, Deewang Bhamidipati, Maria Fox +7
Mathematics · Physics and Astronomy · #11G10 #11G18 #14G35 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #FOS: Mathematics #Nonlinear Waves and Solitons #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2510.01090

openalex publication_date 2025/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• The supersingular locus of the Shimura variety of GU(1,n-1) II
• The supersingular locus of the Shimura variety for GU(1,s)
• Congruence relations for Shimura varieties associated to some unitary groups

Related

• Ekedahl-Oort strata in the GU(q-2,2) Shimura variety
• Stratifications in good reductions of Shimura varieties of abelian type
• On the classification of indecomposable Ekedahl-Oort strata in unitary Shimura varieties, and related Newton polygons
• Ekedahl-Oort strata for good reductions of Shimura varieties of Hodge type
• Ekedahl-Oort stratifications of Shimura varieties via Breuil-Kisin windows