Duke Mathematical Journal

Une correspondance de Jacquet-Langlands p-adique

Gaëtan Chenevier

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Résumé

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.

Abstract

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.

Article information

Source
Duke Math. J., Volume 126, Number 1 (2005), 161-194.

Dates
First available in Project Euclid: 15 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1103136478

Digital Object Identifier
doi:10.1215/S0012-7094-04-12615-6

Mathematical Reviews number (MathSciNet)
MR2111512

Zentralblatt MATH identifier
1070.11016

Subjects
Primary: 11F12, 11F85: $p$-adic theory, local fields [See also 14G20, 22E50]
Secondary: 11F72: Spectral theory; Selberg trace formula 14G22: Rigid analytic geometry

Citation

Chenevier, Gaëtan. Une correspondance de Jacquet-Langlands p -adique. Duke Math. J. 126 (2005), no. 1, 161--194. doi:10.1215/S0012-7094-04-12615-6. https://projecteuclid.org/euclid.dmj/1103136478


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