Abstract: Homological structure of finite modules over regular local rings is fairly well understood. The classical results date back to Serre, Auslander and Buchsbaum. On the other hand, little is known, in general, about the structure of infinite modules. In this talk, we will consider a class of such modules most important from the geometric point of view, namely those that arise as stalks of coherent sheaves over the source of a morphism with regular target. We will sketch the idea how to generalize the classical theory to the case of those modules, by a kind of fibre dimension reduction argument.