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. The authors deduce applications to the Artin and Fontaine-Mazur conjectures. They conclude by constructing Hecke varieties for Hilbert modular forms.
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. The authors deduce applications to the Artin and Fontaine-Mazur conjectures. They conclude by constructing Hecke varieties for Hilbert modular forms.