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.

中文翻译：

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Lubin-Tate 完美体空间中的仿射体和简单的超尖牙表示 II：野生案例

我们在 Lubin-Tate 完美体空间及其形式模型中构建了一个类同形族，使得它们的归约的中间上同调实现了简单的超尖峰表示的局部朗兰兹对应和局部 Jacquet-Langlands 对应。形式模型的约简与某些 Artin-Schreier 变体的完美同构，其上同调实现了原始伽罗瓦表示。我们还展示了与二次形式相关的 Artin-Schreier 变体的 Tate 猜想。