Existence of Gorenstein projective resolutions and Tate cohomology

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Finite Gorenstein representation type implies simple singularity (2007, background): “Theorem C counterposes these developments; it shows that for finitely generated modules, the precovers found in [20] and [15] cannot, in general, be finitely generated.”
Beyond totally reflexive modules and back (2008, background): “For an important class of rings, Jørgensen [78] and Murfet and Salarian [85] prove existence of Gorenstein projective precovers for all modules: Theorem 5.7.”
Acyclicity versus total acyclicity for complexes over noetherian rings (2005, background): “1 These classes fit into a commutative diagram of functors: Kc(PrjR) D⊗R− // Kc(InjR) Df (R) ≀P RHomR(−,D) // Df (R) ≀ I The functor P is induced by the composite K(PrjR) HomR(−,R) −−−−−−−→ K(R) can −−→ D(R) , and it is a theorem of Jørgensen [11] that P is an equivalence of categories.”
Gorenstein Homological Algebra of Artin Algebras (2017, background): “A recent and remarkable result due to Jørgensen states that for a large class of rings such a resolution always exists ([44]).”
Gorenstein complexes and recollements from cotorsion pairs (2012, background): “nctors which is the starting point of the theory; see [EJ00]. Second it leads to a generalized Tate cohomology theory which has been pursued in diﬀerent ways by many authors. See for example [Ben97], [Jør07], [Iac05] and [AM02]. In light of this and Theorem A, it is natural to consider Gorenstein ho”