79 citations · 86 across the 3 of their papers we have counts for
5 papers
On the average number of 2-Selmer elements of elliptic curves over with two marked points
Jack A. Thorne
We consider elliptic curves over global fields of positive characteristic with two distinct marked non-trivial rational points. Restricting to a certain subfamily of the universal…
Elliptic curves over are modular
Jack A. Thorne
We show that if p is a prime, then all elliptic curves defined over the cyclotomic Z_p extension of Q are modular.
Automorphy of some residually dihedral Galois representations
Jack A. Thorne
We establish the automorphy of some families of 2-dimensional representations of the absolute Galois group of a totally real field, which do not satisfy the so-called `Taylor--Wile…
Automorphy of some residually S_5 Galois representations
Chandrashekhar B. Khare, Jack A. Thorne
We prove automorphy lifting theorems for 2-dimensional Galois representations of absolute Galois groups of totally real fields when the residual representation is of "exceptional"…
On the automorphy of -adic Galois representations with small residual image
Jack Thorne
We prove new automorphy lifting theorems for essentially conjugate self-dual Galois representations into . Existing theorems require that the residual representation have 'bi…