Speaker:
Gabor Wiese (University of Luxembourg)
Email:
gabor.wiese@uni.luLocation:
Departamento de Álgebra
Date:
Tue, 19 feb 2019 12:00
Gabor Wiese is professor at the Mathematics Research Unit of the University of Luxembourg. His main areas of interest are Number Theory, Arithmetic Geometry and Computer Algebra. His research focuses on Galois representations (e.g. modularity, congruences, local properties, images, compatible systems, independence).
A two-dimensional representation is called dihedral if it is induced from a character. In the talk I will describe work related to the universal deformation of a dihedral representation over a finite field. In particular, the universal deformation is dihedral itself if and only if any infinitesimal deformation is dihedral. This gives a nice and easy-to-check criterion on when the universal deformation is dihedral. Using class field theory, this criterion gives rise to families of examples of dihedral universal deformations. In favourable situations, one even obtains new R=T-results, as well as new results on Boston's strengthening of the Fontaine-Mazur conjecture. This is joint work with Shaunak V. Deo.