Gorensteinness and Tate Cohomology in Exact Categories

摘要

Motivated by the classical Gorenstein homological theory and structure of Tate cohomology, we develop a theory of Gorenstein projective objects and Tate cohomology in an exact category A with enough projectives. We study some properties of Gorenstein projective objects and establish Tate cohomology of objects with finite Gorenstein projective dimension.