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 …

We study the étale cohomology of Hilbert modular varieties, building on the methods
introduced by Caraiani and Scholze for unitary Shimura varieties. We obtain the analogous …

The goal of these lecture notes is to survey progress on the global Langlands reciprocity
conjecture for $\mathrm {GL} _n $ over number fields from the last decade and a half. We …

The goal of these lecture notes is to survey progress on the global Langlands reciprocity
conjecture for GLn over number fields from the last decade and a half. We highlight results …

A key ingredient in the Taylor–Wiles proof of Fermat's last theorem is the classical Ihara
lemma, which is used to raise the modularity property between some congruent Galois …

In this paper we study certain families of motives, which arise as direct summands of the
cohomology of the Dwork family. We computationally find examples of interesting families …

We prove the classical $ l= p $ local-global compatibility conjecture for certain regular
algebraic cuspidal automorphic representations of weight 0 for GL $ _2 $ over CM fields …

Let $ F $ be a CM field. In this paper, we prove the local-global compatibility for
cohomological cuspidal automorphic representations of $\mathrm {GL} _n (\mathbb {A} _F) …

The modularity of elliptic curves is a concept which percolates through much of modern
number theory. Simply put, an elliptic curve is said to be modular if there exists a transfer of …

Let $ F $ be a CM field, let $ p $ be a prime number. The goal of this paper is to show, under
mild conditions, that the modulo $ p $ cohomology of the locally symmetric spaces $ X $ for …