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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An irreducibility criterion for group representations, with arithmetic applications


Authors: Matteo Longo and Stefano Vigni
Journal: Proc. Amer. Math. Soc. 138 (2010), 3437-3447
MSC (2010): Primary 20C12, 11F80
Published electronically: May 17, 2010
MathSciNet review: 2661544
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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$.


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Additional Information

Matteo Longo
Affiliation: Dipartimento di Matematica Pura e Applicata, Università di Padova, Via Trieste 63, 35121 Padova, Italy
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
Email: stefano.vigni@upc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10485-9
PII: S 0002-9939(2010)10485-9
Keywords: Group representations, Noetherian domains, reductions modulo primes
Received by editor(s): December 23, 2009
Published electronically: May 17, 2010
Communicated by: Ken Ono
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.