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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math f</jats: tex-math>< mml: math xmlns: mml=" http://www. w3. org/1998/Math/MathML"> …

There has been a clear decline in the volume of oxygen in Earth's atmosphere over the past
20 years. Although the magnitude of this decrease appears small compared to the amount of …

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 construct the compatible system of l-adic representations associated to a regular
algebraic cuspidal automorphic representation of GL_n GL n over a CM (or totally real) field …

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 …

Let F be a totally real field, K/F a totally imaginary quadratic extension, d=[F: Q], c∈ Gal (K/F)
the non-trivial Galois automorphism. Let n be a positive integer and G= Gn be the algebraic …

We show that abelian surfaces (and consequently curves of genus 2) over totally real fields
are potentially modular. As a consequence, we obtain the expected meromorphic …

We prove new automorphy lifting theorems for essentially conjugate self-dual Galois
representations into GLn. Existing theorems require that the residual representation have …

We prove the Breuil–Mézard conjecture for two-dimensional potentially Barsotti–Tate
representations of the absolute Galois group (up to the question of determining precise …