An irreducibility criterion for group representations, with arithmetic applications

2010/02/16 by Longo, M., Vigni, S.
#11F80 #20C12 #Commutative Algebra (math.AC) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1002.3150

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.

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