Contents Online
Mathematical Research Letters
Volume 26 (2019)
Number 1
Irreducible components of extended eigenvarieties and interpolating Langlands functoriality
Pages: 159 – 201
DOI: https://dx.doi.org/10.4310/MRL.2019.v26.n1.a9
Authors
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 $\mathrm{GL}_2 / F$, where $F / \mathbb{Q}$ is a cyclic extension, contains non-ordinary components of dimension at least $[F : \mathbb{Q}]$.
C.J. was supported by NSF grant DMS-1128155 and by the Herchel Smith Foundation.
Received 31 March 2017
Accepted 15 January 2018
Published 7 June 2019