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 …

arXiv:2210.01404v2 [math.NT] 1 Feb 2023 Page 1 An introduction to the categorical p-adic
Langlands program Matthew Emerton, Toby Gee, and Eugen Hellmann Abstract. We give an …

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

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 construct projective varieties in mixed characteristic whose singularities model, in
generic cases, those of tamely potentially crystalline Galois deformation rings for unramified …

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 …

We prove the main conjectures of Breuil (J Reine Angew Math, 2012)(including a
generalisation from the principal series to the cuspidal case) and Dembélé (J Reine Angew …

We construct stacks which algebraize Mazur's formal deformation rings of local Galois
representations. More precisely, we construct Noetherian formal algebraic stacks over Spf …

En utilisant le système de Taylor–Wiles–Kisin construit dans un travail récent de Caraiani,
Emerton, Gee, Geraghty, Paškūnas et Shin, nous construisons un analogue de la variété de …