Add to ORKGAbstract. We prove the Sato-Tate conjecture for Hilbert modular forms. More precisely, we prove the natural generalisation of the Sato-Tate conjecture for regular algebraic cuspidal automorphic representations of GL2(AF), F a totally real field, which are not of CM type. The argument is based on the potential automorphy techniques developed by Taylor et. al., but makes use of automorphy lifting theorems over ramified fields, together with a “topological” argument with local deformation rings. In particular, we give a new proof of the conjecture for modular forms, which does not make use of potentia
Let p be a prime number and K a finite extension of Q p. We state conjectures on the smooth represen...
Abstract. Let F be a totally real field and p ≥ 3 a prime. If ρ: Gal(F/F) → GL2(Fp) is continuous, ...
Abstract. We introduce a tensor decomposition of the $\ell$-adic Tate module of an abelian variety $...
Let $F$ be a CM number field. We prove modularity lifting theorems forregular $n$-dimensional Galois...
Let F be a totally real field and p an odd prime. We prove an automorphy lifting theorem for geometr...
This thesis is made up of $3$ separate pieces of work in two themes. In the first half, we prove a ...
We prove many non-generic cases of the Sato-Tate conjecture for abelian surfaces as formulated by Fi...
I do research in number theory and arithmetic geometry, and particularly in the area related to Galo...
We make explicit a construction of Serre giving a definition of an algebraic Sato-Tate group associa...
Abstract. Let p> 2 be prime, and let F be a totally real field in which p is unramified. We give ...
In this thesis, we use the Serre-Tate deformation theory for ordinary abelian varieties to study its...
As the modularity theorem shows, classical modular forms are connected to Tate modules of elliptic c...
We study in this paper Hida's p-adic Hecke algebra for GL_n over a CM field F. Hida has made a conje...
This paper generalises previous work of the author to the setting of overconvergent p-adic automorph...
Abstract. Under mild hypotheses, we prove that if F is a totally real field, and ρ: GF → GL2(Fl) is ...
Let p be a prime number and K a finite extension of Q p. We state conjectures on the smooth represen...
Abstract. Let F be a totally real field and p ≥ 3 a prime. If ρ: Gal(F/F) → GL2(Fp) is continuous, ...
Abstract. We introduce a tensor decomposition of the $\ell$-adic Tate module of an abelian variety $...
Let $F$ be a CM number field. We prove modularity lifting theorems forregular $n$-dimensional Galois...
Let F be a totally real field and p an odd prime. We prove an automorphy lifting theorem for geometr...
This thesis is made up of $3$ separate pieces of work in two themes. In the first half, we prove a ...
We prove many non-generic cases of the Sato-Tate conjecture for abelian surfaces as formulated by Fi...
I do research in number theory and arithmetic geometry, and particularly in the area related to Galo...
We make explicit a construction of Serre giving a definition of an algebraic Sato-Tate group associa...
Abstract. Let p> 2 be prime, and let F be a totally real field in which p is unramified. We give ...
In this thesis, we use the Serre-Tate deformation theory for ordinary abelian varieties to study its...
As the modularity theorem shows, classical modular forms are connected to Tate modules of elliptic c...
We study in this paper Hida's p-adic Hecke algebra for GL_n over a CM field F. Hida has made a conje...
This paper generalises previous work of the author to the setting of overconvergent p-adic automorph...
Abstract. Under mild hypotheses, we prove that if F is a totally real field, and ρ: GF → GL2(Fl) is ...
Let p be a prime number and K a finite extension of Q p. We state conjectures on the smooth represen...
Abstract. Let F be a totally real field and p ≥ 3 a prime. If ρ: Gal(F/F) → GL2(Fp) is continuous, ...
Abstract. We introduce a tensor decomposition of the $\ell$-adic Tate module of an abelian variety $...