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arXiv · 1703.03568

Irreducible components of extended eigenvarieties and interpolating Langlands functoriality

Christian Johansson·James Newton
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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 is a cyclic extension of the rational numbers Q, contains non-ordinary components of dimension at least [F:Q].

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Christian Johansson, James Newton. 2017-03-10. Irreducible components of extended eigenvarieties and interpolating Langlands functoriality. https://arxiv.org/abs/1703.03568

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