An irreducibility criterion for group representations, with arithmetic applications

Longo, Matteo; Vigni, Stefano

doi:10.1090/S0002-9939-2010-10485-9

An irreducibility criterion for group representations, with arithmetic applications
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by Matteo Longo and Stefano Vigni PDF

Proc. Amer. Math. Soc. 138 (2010), 3437-3447 Request permission

Abstract:

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 special attention to universal deformations of residual Galois representations associated with modular forms of weight at least $2$.

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