Affinoids in the Lubin-Tate perfectoid space and simple supercuspidal   representations II: wild case
  We construct a family of affinoids in the Lubin-Tate perfectoid space and their formal models such that the middle cohomology of their reductions realizes the local Langlands correspondence and the local Jacquet-Langlands correspondence for the simple supercuspidal representations. The reductions of the formal models are isomorphic to the perfections of some Artin-Schreier varieties, whose cohomology realizes primitive Galois representations. We show also the Tate conjecture for Artin-Schreier varieties associated to quadratic forms. 
Naoki Imai and Takahiro Tsushima
math.NT math.AG