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

Maria Fox, Naoki Imai

Published 2021-08-08Version 1

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. Moreover we study the intersections of the irreducible components. A stratification of Deligne--Lusztig varieties defined using a power of Frobenius action appears in the description of the intersections.