Homological Dimensions with Respect to a Semidualizing Complex

Abstract

In this paper we build off of Takahashi and White's ${\mathcal{P}}_C$-projective dimension and ${\mathcal{I}}_C$-injective dimension to define these dimensions for when $C$ is a semidaulizing complex. We develop the framework for these homological dimensions by establishing base change results and local-global behavior. Furthermore, we investigate how these dimensions interact with other invariants.

arXiv comment12 pages