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