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Local Langlands correspondence in rigid families

Journal article
Authors Christian Johansson
J. Newton
C. Sorensen
Published in Pacific Journal of Mathematics
Volume 304
Issue 1
Pages 65-102
ISSN 0030-8730
Publication year 2020
Published at Department of Mathematical Sciences
Pages 65-102
Language en
Keywords Eigenvarieties, p-adic automorphic forms, Galois representations, local, Langlands correspondence, adic reductive groups, global compatibility, galois representations, automorphic-forms, kottwitz approach, extensions, modules, program, gl(n), Mathematics
Subject categories Mathematics


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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