On non-abelian Lubin-Tate theory and analytic cohomology
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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.References
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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
- MR Author ID: 1019874
- Email: chojecki@maths.ox.ac.uk
- 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
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 459-471
- MSC (2010): Primary 11F80
- DOI: https://doi.org/10.1090/proc/13716
- MathSciNet review: 3731683