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...

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Veröffentlicht in:	Mathematische annalen 2021-06, Vol.380 (1-2), p.751-788
Hauptverfasser:	Imai, Naoki, Tsushima, Takahiro
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Sprache:	eng
Schlagworte:	Homology Mathematics Mathematics and Statistics Number theory Quadratic forms Representations
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description	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.
doi_str_mv	10.1007/s00208-020-02106-1
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title	Affinoids in the Lubin–Tate perfectoid space and simple supercuspidal representations II: wild case
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