An irreducibility criterion for group representations, with arithmetic applications

Abstract

We prove a criterion for the irreducibility of an integral group representation ρover the fraction field of a noetherian domain R in terms of suitably defined reductions of ρat 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.

11 pages