An irreducibility criterion for group representations, with arithmetic applications

Details An irreducibility criterion for group representations, with arithmetic applications An irreducibility criterion for group representations, with arithmetic applications

2010-02-16

arxiv.org/abs/1002.3150v1

Mathematics

Number Theory

11 pages

Scientific paper

We prove a criterion for the irreducibility of an integral group representation \rho over the fraction field of a noetherian domain R in terms of suitably defined reductions of \rho at prime ideals of R. As applications, we give irreducibility results for universal deformations of residual representations, with a special attention to universal deformations of residual Galois representations associated with modular forms of weight at least 2.

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