IISER Pune
INDIAN INSTITUTE OF SCIENCE EDUCATION AND RESEARCH (IISER) PUNE
where tomorrow’s science begins today
An Autonomous Institution, Ministry of Human Resource Development, Govt. of India
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Seminars and Colloquia

Mathematics

Universal deformation of dihedral representations. 
 
Thu, Nov 01, 2018,   04:30 PM to 05:30 PM at 3rd floor Madhava Hall Mathematics

Dr Shaunak Deo
TIFR MUMBAI

Abstract: Given a 2-dimensional dihedral representation of a profinite
group over a finite field, we will give necessary and sufficient
conditions for its universal deformation to be dihedral. We will then
specialize to the case of absolute Galois group of a number field and
give sufficient conditions for the universal deformation unramified
outside a finite set of primes to be dihedral. We will also see its
applications to unramfied 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.

 

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