Automorphy of some residually dihedral Galois representations
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Abstract
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.
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Journal Title
Mathematische Annalen
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Journal ISSN
0025-5831
1432-1807
1432-1807
Volume Title
364
Publisher
Springer Nature
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Sponsorship
During the period this research was conducted, Jack Thorne served as a Clay Research Fellow.