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arXiv · 2108.03584

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

Maria Fox·Naoki Imai
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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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Maria Fox, Naoki Imai. 2021-08-08. The supersingular locus of the Shimura variety of $\mathrm{GU}(2,n-2)$. https://doi.org/10.1007/s42543-025-00102-5

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