Affinoids in the Lubin-Tate perfectoid space and special cases of the local Langlands correspondence in positive characteristic : announcement (Algebraic Number Theory and Related Topics 2015)

Abstract

This is a research announcement of [To16], where, following the work of Weinstein, Boyarchenko-Weinstein and Imai-Tsushima, we construct a family of affinoids in the Lubin-Tate perfectoid space and formal models such that the ell‐adic cohomology groups of the reductions of the formal models realize the local Langlands correspondence for GL(n) and the local Jacquet‐Langlands correspondence for certain representations related to totally tamely ramified extensions of the base field of degree n. Unlike the preceding work, the base field is assumed to be of positive characteristic in [To16].