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Universal deformations of dihedral representations

October 24, 2018 @ 4:00 pm - 5:00 pm

Given a 2-dimensional dihedral representation of a pronite group over a nite eld, we will give necessary and sucient conditions for its universal deformation to be dihedral. We will then specialize to the case of absolute Galois group of a number eld and give sucient conditions for the universal deformation unramied outside a nite set of primes to be
dihedral. We will also see its applications to unramed Fontaine-Mazur conjecture and to an R=T theorem (in the spirit of Calegari-Geraghty) in the setting of Hilbert modular forms of parallel weight one. We will begin with a brief introduction to the deformation theory of Galois representations. This talk is based on joint work with Gabor Wiese.Discipline/Coordinating Entity: Mathematics

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Date:
October 24, 2018
Time:
4:00 pm - 5:00 pm
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