Versal deformations of pairs and Cohen-Macaulay approximation
For a pair (algebra, module) with isolated singularity we establish the existence of a versal henselian deformation. Obstruction theory in terms of an Andr\'e-Quillen cohomology for pairs is a central ingredient in the Artin theory used. Cohen-Macaulay approximation induces maps between versal base spaces for pairs and cohomology conditions ensure properties like smoothness and isomorphism.