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 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 …

Let p be a prime number, F a totally real number field unramified at places above p and D a
quaternion algebra of center F split at places above p and at no more than one infinite place …

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 …

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 …

Let $ F $ be a totally real field unramified at all places above $ p $ and $ D $ be a quaternion
algebra which splits at either none, or exactly one, of the infinite places. Let $\bar {r}:\mathrm …

Caraiani was supported in part by NSF grant DMS-1501064, by a Royal Society University
Research Fellowship, and by ERC Starting Grant 804176. Emerton was supported in part by …

We prove the weight part of Serre's conjecture in generic situations for forms of U (3) which
are compact at infinity and split at places dividing p as conjectured by Herzig (Duke Math J …