p-adic Deligne--Lusztig spaces

Abstract: I explain how to carry over some definitions and results from classical Deligne--Luzstig theory (for reductive groups over finite fields) to a setup over p-adic fields. More precisely, I discuss p-adic Deligne--Lusztig spaces, defined as certain arc-sheaves on perfect algebras over the residue field, as well as some of their geometric properties. In some cases, one can determine the cohomology of these spaces, and use it to construct smooth representations of p-adic reductive groups geometrically.

algebraic geometrynumber theory

Audience: researchers in the topic

Boston University Number Theory Seminar