On non-abelian Lubin-Tate theory and analytic cohomology

Chojecki, Przemysław

doi:10.1090/proc/13716

On non-abelian Lubin-Tate theory and analytic cohomology
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Proc. Amer. Math. Soc. 146 (2018), 459-471 Request permission

Abstract:

We prove that the $p$-adic local Langlands correspondence for $\operatorname {GL}_2(\mathbb {Q}_p)$ appears in the étale cohomology of the Lubin-Tate tower at infinity. We use global methods using recent results of Emerton on the local-global compatibility, and hence our proof applies to local Galois representations which come via a restriction from global pro-modular Galois representations.

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