The supersingular locus of the Shimura variety of GU(2,n-2)

2021/08/08 by Maria Fox, Naoki Imai, Fox, Maria +1
Mathematics · #11G18 #14M15 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2108.03584

openalex publication_date 2021/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the supersingular locus of a reduction at an inert prime of the Shimura variety attached to GU(2,n-2). More concretely, we realize irreducible components of the supersingular locus as closed subschemes of flag schemes over Deligne--Lusztig varieties defined by explicit conditions after taking perfections. Moreover we study the intersections of the irreducible components. Stratifications of Deligne--Lusztig varieties defined using powers of Frobenius action appear in the description of the intersections.

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