Affinoids in the Lubin-Tate perfectoid space and special cases of the local Langlands correspondence

Abstract

Following Weinstein, Boyarchenko-Weinstein and Imai-Tsushima, we construct a family of affinoids in the Lubin-Tate perfectoid space and formal models such that the cohomology of the reduction of each formal model realizes the local Langlands correspondence and the local Jacquet-Langlands correspondence for certain representations. In the terminology of the essentially tame local Langlands correspondence, the representations treated here are characterized as being parametrized by minimal admissible pairs in which the field extensions are totally ramified.

v2, major revision; main theorem now covers the mixed-characteristic case; "in positive characteristic" in the previous title thus removed; introduction rewritten; several arguments simplified; many errors and typos fixed. v3, more details added; some more errors and typos fixed