Mathematische Annalen | 2021

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.

Volume 380
Pages 751-788
DOI 10.1007/s00208-020-02106-1
Language English
Journal Mathematische Annalen

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