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An irreducibility criterion for group representations, with arithmetic applications

Author(s): Matteo Longo; Stefano Vigni
Journal: Proc. Amer. Math. Soc. 138 (2010), 3437-3447.
MSC (2010): Primary 20C12, 11F80
Posted: 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 in terms of suitably defined reductions of $\rho$ at prime ideals of . 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 .

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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: 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
Posted: May 17, 2010
Communicated by: Ken Ono
Copyright of article: Copyright 2010, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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