Reference : Dihedral Universal Deformations
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Dihedral Universal Deformations
Deo, Shaunak []
Wiese, Gabor mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Research in Number Theory
[en] This article deals with universal deformations of dihedral representations with a particular focus on the question when the universal deformation is dihedral. Results are obtained in three settings: (1) representation theory, (2) algebraic number theory, (3) modularity. As to (1), we prove that the universal deformation is dihedral if all infinitesimal deformations are dihedral. Concerning (2) in the setting of Galois representations of number fields, we give sufficient conditions to ensure that the universal deformation relatively unramified outside a finite set of primes is dihedral, and discuss in how far these conditions are necessary. As a side-result, we obtain cases of the unramified Fontaine-Mazur conjecture. As to (3), we prove a modularity theorem of the form `R=T' for parallel weight one Hilbert modular forms for cases when the minimal universal deformation is dihedral.
Fonds National de la Recherche - FnR

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