The main result of this paper is the existence of Galois representations associated with the
mod p (or mod pm) cohomology of the locally symmetric spaces for GLn over a totally real or …

Let ff be a cuspidal Hecke eigenform of level 1. We prove the automorphy of the symmetric
power lifting Sym nf Sym^nf for every n≥ 1 n≧1. We establish the same result for a more …

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For any reductive group $ G $ over a global function field, we use the cohomology of $ G $-
shtukas with multiple modifications and the geometric Satake equivalence to prove 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 …

Let F be a CM number field. We prove modularity lifting theorems for regular n-dimensional
Galois representations over F without any self-duality condition. We deduce that all elliptic …

We formulate a few conjectures on some hypothetical coherent sheaves on the stacks of
arithmetic local Langlands parameters, including their roles played in the local-global …

We study the locally analytic vectors in the completed cohomology of modular curves and
determine the eigenvectors of a rational Borel subalgebra of. As applications, we prove a …

​ 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 …

In this paper, we establish the modularity of every elliptic curve $ E/F $, where $ F $ runs
over infinitely many imaginary quadratic fields, including $\mathbb {Q}(\sqrt {-d}) $ for $ d= 1 …