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Arithmétique -adique des formes de Hilbert
F. Andreatta, S. Bijakowski, A. Iovita, P. L. Kassaei, V.Pilloni, B. Stroh, Y. Tian, L. Xiao
Astérisque 382 (2016), xxii+266 pages
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Summary

Résumé :
Ce volume est consacré à l'arithmétique -adique des formes modulaires de Hilbert. Il contient plusieurs théorèmes de classicité de formes surconvergentes généralisant d'une part le critère de Coleman, valable en poids assez grand, d'autre part celui de Buzzard-Taylor, valable en poids un, ce dont on déduit des applications aux conjectures d'Artin et de Fontaine-Mazur. On construit également des variétés de Hecke pour les formes de Hilbert.

Mots-clefs : Formes modulaires de Hilbert, formes modulaires -adiques, formes modulaires surconvergentes, représentations galoisiennes, modularité, conjecture d'Artin, conjecture de Fontaine-Mazur.

Abstract:
-adic arithmetic of Hilbert modular forms
This volume is devoted to the study of Hilbert -adic modular forms. It contains classicality theorems for overconvergent forms which generalize on the first hand Coleman criterion, which can be applied in big weights, and on the second hand Buzzard-Taylor criterion, which can be applied in weight one. We deduce applications to the Artin and Fontaine-Mazur conjectures. We finally construct Hecke varieties for Hilbert modular forms.

Class. math. : 37A20, 37D25, 37D30; 37A50, 37C40

ISBN : 978-2-85629-843-5
ISSN : 0303-1179
Publié avec le concours de : Centre National de la Recherche Scientifique

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