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arXiv · 1304.4817

Weak local-global compatibility in the p-adic Langlands program for U(2)

Przemyslaw Chojecki·Claus Sorensen
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Abstract

Inspired by Emerton's work for GL(2), we study the completed cohomology of the tower of finite sets associated with a definite unitary group in two variables. When p splits (and other technical assumptions are fulfilled), we show that the p-adic local Langlands correspondence for GL(2) (over Q_p) occurs in the cohomology. We give an application to the Fontaine-Mazur conjecture over CM fields.

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Przemyslaw Chojecki, Claus Sorensen. 2013-04-17. Weak local-global compatibility in the p-adic Langlands program for U(2). https://arxiv.org/abs/1304.4817

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