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Residually reducible representations of algebras over local Artinian rings

Author(s): Jim Brown
Journal: Proc. Amer. Math. Soc. 136 (2008), 3409-3414.
MSC (2000): Primary 16G10
Posted: June 5, 2008
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Abstract: In this paper we generalize a result of Urban on the structure of residually reducible representations on local Artinian rings from the case that the semi-simplification of the residual representation splits into 2 absolutely irreducible representations to the case where it splits into $ m \geq 2$ absolutely irreducible representations.

References:

[B07]
J. Brown, Saito-Kurokawa lifts and applications to the Bloch-Kato conjecture, Compos. Math. 143, no. 2 (2007), 290-322. MR 2309988

[C94]
H. Carayol, Formes modulaires et représentations galoisiennes à valeurs dans un anneau local complet, Contemp. Math. 165, Amer. Math. Soc., Providence, RI, 1994, 213-237. MR 1279611 (95i:11059)

[U99]
E. Urban, On residually reducible representations on local rings, J. Algebra 212 (1999), 738-742. MR 1676863 (2000a:16020)

[U01]
E. Urban, Selmer groups and the Eisenstein-Klingen ideal, Duke Math. J. 106, no. 3 (2001), 485-525. MR 1813234 (2002b:11073)

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Additional Information:

Jim Brown
Affiliation: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
Address at time of publication: Department of Mathematical Sciences, Clemson University, Clemson, South Carolina 29634-0975
Email: jimlb@caltech.edu

DOI: 10.1090/S0002-9939-08-09568-3
PII: S 0002-9939(08)09568-3
Keywords: Residually reducible representations, Artinian rings
Received by editor(s): June 29, 2007
Posted: June 5, 2008
Communicated by: Wen-Ching Winnie Li
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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