Automorphy of some residually dihedral Galois representations

Thorne, Jack Arfon (2015-05-08)


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–Wiles hypothesis’. We apply this to the problem of the modularity of elliptic curves over totally real fields.