2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66182We 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.LaTeX, 24 Pages, FrenchNumber TheoryRepresentation Theory11F85 (11F12,11F72,14G22)text