This book (1) takes place in a now thirty years long trend of researches, initiated by Ribet
([95]) aiming at constructing “arithmetically interesting” non trivial extensions between global …

Let L be a finite extension of Qp. We construct a (p-adic local Langlands) correspondence
attaching to any irreducible, 2-dimensional, L-representation of GQp, a unitary, admissible …

We produce a canonical filtration for locally free sheaves on an open p-adic annulus
equipped with a Frobenius structure. Using this filtration, we deduce a conjecture of Crew on …

On donne une formalisation de la méthode de Sen pour les représentations $ p $-adiques.
Comme application de ces techniques, on montre que (1) toute représentation $ p $-adique …

Colmez, Pierre. Représentations triangulines de dimension $2 $, dans Représentations $ p
$-adiques de groupes $ p $-adiques I: représentations galoisiennes et $(\varphi,\Gamma) …

​ This book discusses the p-adic modular forms, the eigencurve that parameterize them,
and the p-adic L-functions one can associate to them. These theories and their …

The purpose of this article is to give formulas for Bloch-Kato's exponential map and its dual
for an absolutely crystalline padic representation V, in terms of the (ϕ, Γ)-module associated …

The present book is a new revised and updated version of “Number Theory I. Introduction to
Number Theory” by Yu. I. Manin and AA Panchishkin, appeared in 1989 in Moscow (VINITI …

The slope filtration theorem gives a partial analogue of the eigenspace decomposition of a
linear transformation, for a Frobenius-semilinear endomorphism of a finite free module over …

Si M est un motif défini sur un corps de nombres, on sait lui associer (au moins
conjecturalement) une fonction analytique complexe L (M, s) définie par un produit eulérien …