Good reduction of affinoids for epipelagic representations in the Lubin-Tate perfectoid space I: tame case

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