Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 20C12, 11F80

Retrieve articles in all journals with MSC (2010): 20C12, 11F80

Additional Information

Matteo Longo
Affiliation: Dipartimento di Matematica Pura e Applicata, Università di Padova, Via Trieste 63, 35121 Padova, Italy

Stefano Vigni
Affiliation: Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, C. Jordi Girona 1-3, 08034 Barcelona, Spain

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.

American Mathematical Society