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 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 …

We formulate a number of related generalisations of the weight part of Serre's conjecture to
the case of GLn over an arbitrary number field, motivated by the formalism of the Breuil …

We prove a variety of results on the existence of automorphic Galois representations lifting a
residual automorphic Galois representation. We prove a result on the structure of …

We prove the Sato-Tate conjecture for Hilbert modular forms. More precisely, we prove the
natural generalisation of the Sato-Tate conjecture for regular algebraic cuspidal …

The p-adic local Langlands correspondence for GL_2 (Q_p) is given by an exact functor
from unitary Banach representations of GL_2 (Q_p) to representations of the absolute Galois …

We prove the Ramanujan and Sato-Tate conjectures for Bianchi modular forms of weight at
least 2. More generally, we prove these conjectures for all regular algebraic cuspidal …

The emerging p-adic Langlands programme Page 1 Proceedings of the International Congress
of Mathematicians Hyderabad, India, 2010 The emerging p-adic Langlands programme …

We show that Colmez's functor from GL2 (QP) representations to Gqp representation
produces essentially all two dimensional representations of Gqp. The method compares the …