On residually reducible representations on local rings
type: Item
instance of: scholarly article
title: On residually reducible representations on local rings
zbMATH Open document ID: 0996.16007
published in: Journal of Algebra
publication date: 1999-05-26T00:00:00Z
review text: Let \(A\) be a local Artinian ring with maximal ideal \(\mathcal M\), let \(R\) be an \(A\)-algebra and let \(\rho\) be an \(A\)-representation of \(R\). If the residual representation \(\overline\rho\) (that is, with values in the residue field) is absolutely irreducible, then it is well-known by a result of Carayol that \(\rho\) is completely determined by its trace. This is no longer true in the reducible case. The author proves a version of this result assuming some further hypothesis.
Mathematics Subject Classification ID: 16G10
Mathematics Subject Classification ID: 16P20
zbMATH DE Number: 1271830
zbMATH Keywords: reducible representations
zbMATH Keywords: local Artinian rings
zbMATH Keywords: traces
author: Eric Urban
reviewed by: Flávio U. Coelho
MaRDI profile type: Publication
full work available at URL: jabr.1998.7635
OpenAlex ID: W2090569851
cites work: Q4314335
cites work: Selmer groups and the Eisenstein-Klingen ideal.
DOI: 10.1006/JABR.1998.7635
description: scientific article; zbMATH DE number 1271830