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On $\text{mod}~p$ non-abelian Lubin–Tate theory for  $\text{GL}_{2}(\mathbb{Q}_{p})$

  • Przemysław Chojecki (a1) (a2)

Abstract

We analyse the $\text{mod}~p$ étale cohomology of the Lubin–Tate tower both with compact support and without support. We prove that there are no supersingular representations in the $H_{c}^{1}$ of the Lubin–Tate tower. On the other hand, we show that in $H^{1}$ of the Lubin–Tate tower appears the $\text{mod}~p$ local Langlands correspondence and the $\text{mod}~p$ local Jacquet–Langlands correspondence, which we define in the text. We discuss the local-global compatibility part of the Buzzard–Diamond–Jarvis conjecture which appears naturally in this context.

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On $\text{mod}~p$ non-abelian Lubin–Tate theory for  $\text{GL}_{2}(\mathbb{Q}_{p})$

  • Przemysław Chojecki (a1) (a2)

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