On the Supersingular Locus of the $\mathrm{GU}(2,n-2)$ Shimura Variety

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 decompose the supersingular locus into a disjoint union of iterated fibrations over (classical) Deligne-Lusztig varieties after taking perfection. As an immediate application, when $p\ge 3$, we prove an analogue of Oort's conjecture on the supersingular locus of the Siegel modular variety.

32 pages. An application is added