We prove several results about p-divisible groups and Rapoport-Zink spaces. Our main goal
is to prove that Rapoport-Zink spaces at infinite level are naturally perfectoid spaces, and to …

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 …

In this paper, we associate to every p-adic representation V ap-adic differential equation D†
rig (V), that is to say a module with a connection over the Robba ring. We do this via the …

Following ideas of Berger and Breuil, we give a new classification of crystalline
representations. The objects involved may be viewed as local, characteristic 0 analogues of …

We prove that, under some mild conditions, a two dimensional p-adic Galois representation
which is residually modular and potentially Barsotti-Tate at p is modular. This provides a …

Sur quelques représentations modulaires et p -adiques de GL 2 ( Q p ): I Page 1 Sur
quelques repre“sentations modulaires et p-adiques de GL 2 šQpŽ: I šOn Some Modular …

We prove a conjecture of Fontaine and Mazur on modularity of representations of G ℚ which
are potentially semi-stable at p, for representations coming from finite slope, overconvergent …

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

Cet article est le résultat d'une relecture de la démonstration de la conjecture {\fontencoding
{U}\fontfamily {lasy}\selectfont (\kern-0.20 em (\kern. 175em} faiblement admissible implique …

Nous conjecturons que la réduction modulo des représentations cristallines irréductibles de
dimension 2 sur peut être prédite par la réduction modulo. Nous explicitons quelques …