Local Langlands correspondence in rigid families

We show that local-global compatibility (at split primes) away from $p$ holds at all points of the $p$ -adic eigenvariety of a definite $n$ -variable unitary group. We do this by interpolating the local Langlands correspondence for ${GL}_{n}$ across the eigenvariety by considering the fibers of its defining coherent sheaf. We employ techniques of Chenevier and Scholze used in Scholze’s proof of the local Langlands conjecture for ${GL}_{n}$ .

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Keywords

Eigenvarieties, p-adic automorphic forms, Galois representations, local Langlands correspondence

Mathematical Subject Classification 2010

Primary: 11F70

Secondary: 11F80

Milestones

Received: 12 October 2018

Revised: 15 July 2019

Accepted: 1 August 2019

Published: 18 January 2020

Authors

Christian Johansson
Department of Mathematical Sciences Chalmers University of Technology and the University of Gothenburg SE-412 96 Gothenburg Sweden

James Newton
Department of Mathematics King’s College London Strand London United Kingdom

Claus Sorensen
Department of Mathematics University of California, San Diego La Jolla, CA United States

Vol. 304, No. 1, 2020

Christian Johansson, James Newton and Claus Sorensen

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors