Irreducible components of extended eigenvarieties and interpolating Langlands functoriality
arXiv:1703.03568
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].
23 pages, v2: some minor corrections and changes. A new section (3.4) gives the construction of an eigenvariety which is independent of the choice of controlling 'U_p' operator