Irreducible components of extended eigenvarieties and interpolating Langlands functoriality
Mathematical Research Letters
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Johansson, H. C., & Newton, J. Irreducible components of extended eigenvarieties and interpolating Langlands functoriality. Mathematical Research Letters https://doi.org/10.17863/CAM.30273
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].
This record's DOI: https://doi.org/10.17863/CAM.30273
This record's URL: https://www.repository.cam.ac.uk/handle/1810/282910