Une correspondance de Jacquet-Langlands p-adique

By Gaëtan Chenevier. 2003

87 citations recorded by the source corpus.

We extend the Jacquet-Langlands'correspondence between the Hecke-modules of usual and quaternionic modular forms, to overconvergent p-adic forms of finite slope. We show that this correspondence respects p-adic families and is induced by an isomorphism between some associated eigencurves.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0d2ae87f852ee4eff60bc8e0a6f1057a2c0ac585

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

On the eigencurve at classical weight $1$ points (2013, background): “There exists (see [6, § 7]) a continuous pseudo-character sending Frob ℓ to T ℓ for all ℓ ∤ Np .”
The eigencurve over the boundary of weight space (2014, result): “normalization of the former (and possibly changing some non-reduced structure). Remark 1.7. We remark on the relation to the literature. 4 (1)By G. Chenevier’s p-adic Jacquet{Langlands correspondence [Ch05], we can translate results from the case of automorphic forms for denite quaternion algebras t”