Reference : Dihedral Universal Deformations
Scientific Presentations in Universities or Research Centers : Scientific presentation in universities or research centers
Physical, chemical, mathematical & earth Sciences : Mathematics
Dihedral Universal Deformations
Wiese, Gabor mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Seminar of Algebra, University of Sevilla
19 February 2019
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.

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