Complete flat resolutions, Tate homology and the depth formula

Abstract

We introduce Tate homology of complexes of finite Gorenstein flat dimension based on complete flat resolutions and give a new method of computing Tate homology in Christensen and Jorgensen's sense. We also investigate the relationship between Tate homology and Tate cohomology. As an application, a more brief proof of the main result on derived depth formula of [Vanishing of Tate homology and depth formula over local rings, J. Pure Appl. Algebra 219 (2015) 464-481] is given.