An irreducibility criterion for group representations, with arithmetic applications
Abstract
We prove a criterion for the irreducibility of an integral group representation over the fraction field of a noetherian domain R in terms of suitably defined reductions of 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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