The Artinian Berger Conjecture

Abstract

We propose an Artinian version of Berger s Conjecture for curves, concerning the module of Kahler differentials of an algebra. Our version implies Berger’s Conjecture in characteristic 0. We establish our Artinian Berger Conjecture in a number of cases, and prove that Berger’s Conjecture holds for curve singularities whose conductor ideal contains the cube of a maximal ideal.