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15 January 2005 Une correspondance de Jacquet-Langlands p-adique
Gaëtan Chenevier
Duke Math. J. 126(1): 161-194 (15 January 2005). DOI: 10.1215/S0012-7094-04-12615-6

Abstract

La correspondance de Jacquet-Langlands établit une bijection Hecke-équivariante entre les espaces de formes modulaires quaternioniques et certains espaces de formes modulaires usuelles. Dans cet article, nous montrons qu'elle se prolonge en un isomorphisme rigide analytique entre des courbes de Hecke définies de part et d'autre, de sorte qu'elle s'étend aux formes p-adiques surconvergentes de pente finie, ainsi qu'aux familles p-adiques.

In this paper, we extend the Jacquet-Langlands correspondence between Hecke-modules of usual modular forms 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.

Citation

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Gaëtan Chenevier. "Une correspondance de Jacquet-Langlands p-adique." Duke Math. J. 126 (1) 161 - 194, 15 January 2005. https://doi.org/10.1215/S0012-7094-04-12615-6

Information

Published: 15 January 2005
First available in Project Euclid: 15 December 2004

zbMATH: 1070.11016
MathSciNet: MR2111512
Digital Object Identifier: 10.1215/S0012-7094-04-12615-6

Subjects:
Primary: 11F12,, 11F85
Secondary: 11F72, 14G22

Rights: Copyright © 2005 Duke University Press

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Vol.126 • No. 1 • 15 January 2005
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