We prove new cases of the Fontaine-Mazur conjecture, that a $2 $-dimensional $ p $-adic
representation $\rho $ of $ G_ {\mathbb {Q}, S} $ which is potentially semi-stable at $ p …

In 1987 Serre conjectured that any mod ℓ 2-dimensional irreducible odd representation of
the absolute Galois group of the rationals came from a modular form in a precise way. We …

The authors construct new families of smooth admissible $\overline {\mathbb {F}} _p $-<
WBR> representations of $\mathrm {GL} _2 (F) $, where $ F $ is a finite extension of …

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 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 conjecture generalising the weight in Serre's Conjecture to n-dimensional
representations ρ: Gal ([special characters omitted])→ GL n ([special characters omitted]) …

We prove a variety of results on the existence of automorphic Galois representations lifting a
residual automorphic Galois representation. We prove a result on the structure of …

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 …

The emerging p-adic Langlands programme Page 1 Proceedings of the International Congress
of Mathematicians Hyderabad, India, 2010 The emerging p-adic Langlands programme …

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 …