Homological invariants over non-positive DG-rings

Abstract

This paper explores various notions of projective, injective and flat dimensions, and the different versions of each dimension are compared to each other. Homological characterizations of these dimensions are provided in terms of bounded resolutions and vanishing of appropriate derived functors over a non-positive DG-ring. Some homological identities related to these homological invariants, such as Auslander–Buchsbaum formula, Bass formula and derived depth formula, are proved over a commutative Noetherian DG-ring.