Abstract
Let A be a local Artinian ring with maximal ideal M and residual field k . Let R be an A-algebra. We mean by an n-dimensional A-representaŽ . tion of R any homomorphism of A-algebra r from R to M A . For such n a representation, we denote by r the residual representation with values in Ž . M k . It is proven by Carayol that such a representation, if r is absolutely n irreducible, is completely determined by its trace. In the reducible case, Ž one cannot generalize this theorem without assuming more hypothesis see w x. the counterexample given in 1 . The purpose of this note is to give a generalization in the reducible case. It is the best generalization one can Ž . get see remarks .
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