Affinoids in the Lubin–Tate Perfectoid Space and Simple Supercuspidal Representations I: Tame Case

Abstract

We construct a family of affinoids in the Lubin-Tate perfectoid space and their formal models such that the middle cohomology of the reductions of the formal models realizes the local Langlands correspondence and the local Jacquet-Langlands correspondence for simple supercuspidal representations in the case where the dimension of Galois representations is prime to the residue characteristic. The reductions of the formal models are isomorphic to the perfections of Artin-Schreier varieties associated to quadratic forms.