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

Abstract: The irreducible components of the supersingular locus of a reduction at an inert prime of the Shimura variety attached to $\mathrm{GU}(1, n-1)$ was studied by Vollaard-Wedhorn. In the case of $\mathrm{GU}(2, n-2)$, it was studied by Howard-Pappas if $n=4$, but the situation is completely different if $n>4$. We discuss this question for $n>4$ in terms of affine Deligne-Lusztig varieties. This is a joint work with Maria Fox.

algebraic geometrynumber theory

Audience: researchers in the topic

Séminaire de géométrie arithmétique et motivique (Paris Nord)