The Jacquet-Langlands correspondence for overconvergent Hilbert modular forms

Abstract

We use results by Chenevier to interpolate the classical Jacquet-Langlands correspondence for Hilbert modular forms, which gives us an extension of Chenevier's results to totally real fields. From this we obtain an isomorphisms between eigenvarieties attached Hilbert modular forms and those attached to modular forms on a totally definite quaternion algebra over a totally real field of even degree.

22 pages. Final Version, to appear in Int. J. Number Theory

References in corpus (1)

• The eigencurve over the boundary of weight space

Cited by in corpus (2)

• A $p$-adic adjoint $L$-function and the ramification locus of the Hilbert modular eigenvariety
• $2$-adic slopes of Hilbert modular forms over $\mathbb{Q}(\sqrt{5})$