Gorenstein homological dimensions

TL;DR: This paper develops a homological theory of representations with pure acyclic injective resolutions, characterizing strongly fp-injective representations and defining relative Gorenstein injective representations, with applications to model structures in representation categories.

TL;DR: In this paper, the balance of the Gorenstein Tor-functor for modules of finite projective, injective and flat dimensions has been investigated for a class of rings with global and weak dimensions, in terms of certain cohomological invariants of the ring.

TL;DR: Gorenstein tilting approximations as discussed by the authors have been used to study the existence of complements to partial Gorenstein tilts and their associated relative cotorsion pairs, as well as some connections between finitistic dimension conjectures.

TL;DR: In this article, three constitutive exact subcategories of Adelman's free abelian category Ab ( A ) over a Quillen exact category A, which provide an intrinsic description of Ab( A ) and encapsulate the mechanism of (finite or infinite) tilting are presented.

TL;DR: In this article, a self-contained treatment of modules of finite G-dimension, established basic properties of relative and Tate cohomology, and embed the comparison morphisms into a canonical long exact sequence.

TL;DR: Auslander and Buchweitz as mentioned in this paper show that for any finitely generated R-module N there exists an amaximal Cohen-Macaulay R-modules M which surjects onto N and such that any othersurjection from a maximal Cohen-macaulay module onto N factors over it.