An irreducibility criterion for group representations, with arithmetic applications
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- by Matteo Longo and Stefano Vigni PDF
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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 $2$.References
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Additional Information
- Matteo Longo
- Affiliation: Dipartimento di Matematica Pura e Applicata, Università di Padova, Via Trieste 63, 35121 Padova, Italy
- MR Author ID: 790759
- Email: mlongo@math.unipd.it
- Stefano Vigni
- Affiliation: Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, C. Jordi Girona 1-3, 08034 Barcelona, Spain
- MR Author ID: 842395
- Email: stefano.vigni@upc.edu
- Received by editor(s): December 23, 2009
- Published electronically: May 17, 2010
- Communicated by: Ken Ono
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 3437-3447
- MSC (2010): Primary 20C12, 11F80
- DOI: https://doi.org/10.1090/S0002-9939-2010-10485-9
- MathSciNet review: 2661544