Automorphy of some residually dihedral Galois representations

2015/04/04 by Jack A. Thorne, Thorne, Jack A.
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1504.00994

To appear in Mathematische Annalen. arXiv admin note: text overlap with arXiv:1503.03796

arxiv created 2015/04/04 · openalex publication_date 2015/04/04 · arxiv updated 2015/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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

Citations

• Automorphy of some residually S₅ Galois representations

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