Reference : Modularity of certain 2-dimensional mod p^n representations of Gal(Qbar/Q
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Modularity of certain 2-dimensional mod p^n representations of Gal(Qbar/Q
Adibhatla, Rajender mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
HIM Trimester on Arithmetic and Geometry
HIM, Bonn
[en] modualr forms ; Galois representations
[en] For an odd rational prime p and integer n>1, we consider certain continuous representations rho_n of G_Q into GL_2(Z/p^nZ) with fixed determinant, whose local restrictions "look" like they arise from modular Galois representations, and whose mod p reductions are odd and irreducible. Under suitable hypotheses on the size of their images, we use deformation theory to lift rho_n to rho in characteristic 0. We then invoke a modularity lifting theorem of Skinner-Wiles to show that rho is modular.
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