This paper is the first part of a work which proves Serre's modularity conjecture. We first
prove the cases p\not=2 and odd conductor, and p= 2 and weight 2, see Theorem 1.2 …

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 …

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 …

Serre’s modularity conjecture (II) Page 1 Invent math (2009) 178: 505–586 DOI 10.1007/s00222-009-0206-6
Serre’s modularity conjecture (II) Chandrashekhar Khare · Jean-Pierre Wintenberger …

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 …

We construct a Euler system in the cohomology of the tensor product of the Galois
representations attached to two modular forms, using elements in the higher Chow groups of …

Limites de représentations cristallines Page 1 Compositio Math. 140 (2004) 1473–1498
DOI: 10.1112/S0010437X04000879 Limites de représentations cristallines Laurent Berger …

In Fall 2003, Jean-Marc Fontaine was appointed as Chair Professor of Arithmetic Geometry
at Tsinghua University in Beijing. This was the starting point of broad Sino-French …

Understanding Galois representations is one of the central goals of number theory. Around
1990, Fontaine devised a strategy to compare such p-adic Galois representations to …

We prove the level one case of Serre's conjecture. Namely, we prove that any continuous,
odd, irreducible representation ρ ̲: GQ→ GL 2 (F p ̲) which is unramified outside p arises …