Finiteness criteria in Gorenstein homological algebra

Ioannis Emmanouil and Olympia Talelli

Abstract. In this paper, we examine the class of modules of finite Gorenstein projective
dimension and study approximations of modules in that class by modules, which are either
Gorenstein projective or else have finite projective dimension. We also examine the relevance
of complete cohomology in the study of modules of finite Gorenstein projective dimension and
obtain, over group rings, such a finiteness criterion that involves only complete cohomology.