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On non-abelian Lubin-Tate theory and analytic cohomology


Author: Przemysław Chojecki
Journal: Proc. Amer. Math. Soc. 146 (2018), 459-471
MSC (2010): Primary 11F80
DOI: https://doi.org/10.1090/proc/13716
Published electronically: October 30, 2017
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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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Additional Information

Przemysław Chojecki
Affiliation: Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom
Address at time of publication: Polish Academy of Sciences, ul. Sniadeckich 8 00-656, Warszawa, Poland
Email: chojecki@maths.ox.ac.uk

DOI: https://doi.org/10.1090/proc/13716
Received by editor(s): April 18, 2016
Received by editor(s) in revised form: November 27, 2016, and February 20, 2017
Published electronically: October 30, 2017
Communicated by: Romyar T. Sharif
Article copyright: © Copyright 2017 American Mathematical Society

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