Absolute, Relative, and Tate Cohomology of Modules of Finite Gorenstein Dimension

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Gorenstein projective dimension for complexes (2004, methodology): “It is obtained by blending the approach of Enochs and Jenda to Gorenstein projective dimension of modules with that of Avramov and Martsinkovsky [6] to Gorenstein dimension of finite modules over noetherian rings.”
Existence of Gorenstein projective resolutions and Tate cohomology (2007, methodology): “2) coincide with the previously defined Tate cohomology groups from [3] and[26] (see Remark3.”
Independence of the Total Reflexivity Conditions for Modules (2004, background): “As noted by Avramov and Martsinkovsky in [4], the module M is totally reflexive if and only if it satisfies (TRi) for all i, except possibly for i = 1 or i = −1.”
Generalized Tate cohomology (2005, background): “Since $0\rightarrow C\rightarrow\overline{M(u)}\rightarrow P[1]\rightarrow 0$ is exact and both $P$ and $C$ are exact complexes, the exactness of $\overline{M(u)}$ follows.”