Let F be a CM number field. We prove modularity lifting theorems for regular n-dimensional
Galois representations over F without any self-duality condition. We deduce that all elliptic …

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 …

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 …

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 new cases of Fontaine-Mazur conjecture on two-dimensional Galois
representations over $\mathbb {Q} $ when the residual representation is reducible. Our …

We associate infinitesimal characters to (twisted) families of $ L $-parameters and $ C $-
parameters of $ p $-adic reductive groups. We use the construction to study the action of the …

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 $ 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 …

Under a stronger genericity condition, we prove the local analogue of ghost conjecture of
Bergdall and Pollack. As applications, we deduce in this case (a) a folklore conjecture of …