On residually reducible representations on local rings
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.
scientific article; zbMATH DE number 1271830