Gorenstein derived equivalences and their invariants

The main objective of this paper is to study the relative derived categories from various points of view. Let AA be an abelian category and CC be a contravariantly finite subcategory of AA. One can define CC-relative derived category of AA, denoted by DC⁎(A). The interesting case for us is when AA has enough projective objects and C=GP-AC=GP-A is the class of Gorenstein projective objects, where DC⁎(A) is known as the Gorenstein derived category of AA. We explicitly study the relative derived categories, specially over artin algebras, present a relative version of Rickardʼs theorem, specially for Gorenstein derived categories, provide some invariants under Gorenstein derived equivalences and finally study the relationships between relative and (absolute) derived categories.