Irreducible components of extended eigenvarieties and interpolating Langlands functoriality
Journal article, 2019

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 GL2/F, where F/Q is a cyclic extension, contains non-ordinary components of dimension at least [F : Q] .


Christian Johansson

Chalmers, Mathematical Sciences, Algebra and geometry

University of Gothenburg

James Newton

King's College London

Mathematical Research Letters

1073-2780 (ISSN)

Vol. 26 1 159-201

Subject Categories

Algebra and Logic


Mathematical Analysis



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