5 papers
Towards the Fontaine--Mazur conjecture for GL(2)
Jack A. Thorne
We combine a new type of modularity result with the geometry of numbers in order to prove some new cases of the Fontaine--Mazur conjecture for GL(2).
Adjoint Bloch--Kato Selmer groups of regular algebraic automorphic Galois representations
Lambert A'Campo, Bence Hevesi, Jack A. Thorne +1
The paper proves that the adjoint Bloch–Kato Selmer group of Galois representations attached to regular algebraic automorphic representations of GL_n over CM fields is zero, using…
Local-global compatibility of automorphic Galois representations over CM fields at
Lambert A'Campo, Bence Hevesi, Jack A. Thorne +1
The paper proves that Galois representations attached to cuspidal regular algebraic automorphic representations of GL_n over CM fields are potentially semi‑stable and match the loc…
The Ramanujan and Sato-Tate Conjectures for Bianchi modular forms
George Boxer, Frank Calegari, Toby Gee +2
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 autom…
Symmetric power functoriality for Hilbert modular forms
James Newton, Jack A. Thorne
Let be a totally real field. We prove the existence of all symmetric power liftings of those cuspidal automorphic representations of associated to…