Vol. 304, No. 1, 2020

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Local Langlands correspondence in rigid families

Christian Johansson, James Newton and Claus Sorensen

Vol. 304 (2020), No. 1, 65–102
Abstract

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 GLn 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 GLn.

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