We describe a new approach to relative p-adic Hodge theory based on systematic use of
Witt vector constructions and nonarchimedean analytic geometry in the style of both …

1.1. The local-global compatibility conjecture. Fix a prime p, as well as a finite extension E of
Qp. If Kp is an open subgroup of GL2 (Zp)(referred to as a “tame level”), then one can define …

We prove the finiteness and compatibility with base change of the $(\varphi,\Gamma) $-
cohomology and the Iwasawa cohomology of arithmetic families of $(\varphi,\Gamma) …

We prove new cases of the Fontaine-Mazur conjecture, that a $2 $-dimensional $ p $-adic
representation $\rho $ of $ G_ {\mathbb {Q}, S} $ which is potentially semi-stable at $ p …

In 1987 Serre conjectured that any mod ℓ 2-dimensional irreducible odd representation of
the absolute Galois group of the rationals came from a modular form in a precise way. We …

Patching and the p-adic local Langlands correspondenceT1 Page 1 arXiv:1310.0831v5 [math.NT]
1 Jul 2016 Cambridge Journal of Mathematics Volume 0, Number 0, 1, 2014 Patching and the …

We prove a conjecture of Colmez concerning the reduction modulo p of invariant lattices in
irreducible admissible unitary p-adic Banach space representations of GL2 (Q p) with p≥ 5 …

The authors construct new families of smooth admissible $\overline {\mathbb {F}} _p $-<
WBR> representations of $\mathrm {GL} _2 (F) $, where $ F $ is a finite extension of …

In a previous paper, we constructed a category of (phi, Gamma)-modules associated to any
adic space over Q_p with the property that the etale (phi, Gamma)-modules correspond to …

If G is a connected reductive p-adic group, P is a parabolic subgroup of G, and M is a Levi
factor of P, and if A is an Artinian local ring having a finite residue field of characteristic p …