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The supersingular locus of the Shimura variety of $\mathrm{GU}(2,n-2)$

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arxiv 2108.03584 v3 pith:DGZJJG2M submitted 2021-08-08 math.NT math.AG

Maria Fox , Naoki Imai This is my paper · ORCID
classification math.NTmath.AG
keywords locussupersingularcomponentsdefineddeligne--lusztigintersectionsirreduciblemathrm
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abstract

We study the supersingular locus of a reduction at an inert prime of the Shimura variety attached to $\mathrm{GU}(2,n-2)$. 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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  1. The cohomology of certain intermediate strata of Kottwitz varieties

    math.NT 2025-07 conditional novelty 6.0 of 10

    The Frobenius-Hecke trace on the cohomology of two-slope Newton strata of compact unitary Kottwitz varieties is expressed as an explicit finite sum over type I and type II automorphic representations.

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