Gorensteinness, homological invariants and Gorenstein derived categories

Abstract

Relations between Gorenstein derived categories, Gorenstein defect categories and Gorenstein stable categories are established. Using these, the Gorensteinness of an algebra A and invariants with respect to recollements of the bounded Gorenstein derived category Dgpb (A-mod) of A are investigated. Specifically, the Gorensteinness of A is characterized in terms of recollements of Dgpb(A-mod) and Gorenstein derived equivalences. It is also shown that Cohen-Macaulay-finiteness is invariant with respect to the recollements of Dgpb(A-mod).