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 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 …

We prove the Ramanujan and Sato-Tate conjectures for Bianchi modular forms of weight at
least 2. More generally, we prove these conjectures for all regular algebraic cuspidal …

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 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 …

We prove the weight elimination direction of the Serre weight conjectures as formulated by
Herzig for forms of U (n) which are compact at infinity and split at places dividing p in generic …