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Irreducible components of extended eigenvarieties and interpolating Langlands functoriality

Journal article
Authors Christian Johansson
J. Newton
Published in Mathematical Research Letters
Volume 26
Issue 1
Pages 159-201
ISSN 1073-2780
Publication year 2019
Published at Department of Mathematical Sciences
Pages 159-201
Language en
Links dx.doi.org/10.4310/MRL.2019.v26.n1....
Keywords automorphy, families, Mathematics
Subject categories Mathematics

Abstract

We study the basic geometry of a class of analytic adic spaces that arise in the study of the extended (or adic) eigenvarieties constructed by Andreatta-Iovita-Pilloni, Gulotta and the authors. We apply this to prove a general interpolation theorem for Langlands functoriality, which works for extended eigenvarieties and improves upon existing results in characteristic 0. As an application, we show that the characteristic p locus of the extended eigenvariety for GL(2)/F, where F/Q is a cyclic extension, contains non-ordinary components of dimension at least [F : Q].

Page Manager: Webmaster|Last update: 9/11/2012
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