Arithmétique p-adique des formes de Hilbert
By: Fabrizio Andreatta, Stéphane Bijakowski, Adrian Iovita, Payman L. Kassaei, Vincent Pilloni, Benoît Stroh, Yichao Tian & Liang Xiao
Contributors: Bijakowski, Stéphane, author; Iovita, Adrian, author; Kassaei, Payman L., 1973- author; Pilloni, Vincent, author; Stroh, Benoît, author; Tian, Yichao, author; Xiao, Liang, author
Series: Astérisque -- 382; Astérisque -- 382.
Publisher: Société mathématique de France
Published: 2016
Place of publication: Paris
Language: eng; fre
Number of pages: 266
ISBN-13: 9782856298435
Subjects: Modular Forms; Hilbert modular surfaces; Discontinuous groups; Automorphic forms; Arithmetical algebraic geometry; Shimura varieties
Description: This volume is devoted to the study of Hilbert p-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.
Notes: Includes bibliographical references.

Text in English and French.