On the structure of the set of semidualizing complexes

Abstract

We study the structure of the set of semidualizing complexes over a local ring. In particular, we prove that for a pair of semidualizing complexes $X_1$ and $X_2$ such that $G_{X_{2}}\dim X_{1}<\infty $ we have $X_2\simeq X_1\otimes^{L}_R\func{\mathbf{R}Hom}_R(X_{1},X_{2})$. Specializing to the case of semidualizing modules over artinian rings we obtain a number of quantitative results for rings possessing a configuration of semidualizing modules of special form. For rings with ${\mathfrak m}^3=0$ this condition reduces to the existence of a nontrivial semidualizing module and we prove a number of structural results in this case.