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arXiv · 1610.09711

The Jacquet-Langlands correspondence for overconvergent Hilbert modular forms

Christopher Birkbeck
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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.

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Christopher Birkbeck. 2018-11-12. The Jacquet-Langlands correspondence for overconvergent Hilbert modular forms. https://doi.org/10.1142/s1793042119500258

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