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

A GEOMETRIC PERSPECTIVE ON THE BREUIL–MÉZARD CONJECTURE Page 1 J. Inst. Math.
Jussieu (2014) 13(1), 183–223 183 doi:10.1017/S147474801300011X c Cambridge University …

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 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 study G-valued Galois deformation rings with prescribed properties, where G is an
arbitrary (not necessarily connected) reductive group over an extension of ℤ l for some …

Let $ p> 2$ be prime. We prove the weight part of Serre's conjecture for rank two unitary
groups for mod $ p $ representations in the unramified case (that is, the Buzzard–Diamond …

Let p be a prime number and K a finite extension of Q p. We state conjectures on the smooth
representations of GL n (K) that occur in spaces of mod p automorphic forms (for compact …

Under an assumption on the existence of p-adic Galois representations, we carry out Taylor–
Wiles patching (in the derived category) for the completed homology of the locally symmetric …

Let p> 2 be prime. We use purely local methods to determine the possible reductions of
certain two-dimensional crystalline representations, which we call pseudo-Barsotti–Tate …