Lefschetz operator and local Langlands mod ℓ: The regular case

Abstract

Let $p$ and $\ell$ be two distinct primes. The aim of this paper is to show how, under a certain congruence hypothesis, the mod $\ell$ cohomology complex of the Lubin-Tate tower, together with a natural Lefschetz operator, provides a geometric interpretation of Vignéras’s local Langlands correspondence modulo $\ell$ for unipotent representations.