Dualizing complexes and homomorphisms vanishing in Koszul homology (Q494972)

The author extends a result of [\textit{S. Nasseh} and \textit{S. Sather-Wagstaff}, Czech. Math. J. 65, No. 3, 837--865 (2015; Zbl 1363.13002)]. More explicitly, the following is the main result of the paper under review: Theorem. Let C be a semidualizing complex over a noetherian local ring A. If there exists a local homomorphism \(A\to B\) vanishing at the level of the first Koszul homology modules (e.g., the Frobenius endomorphism in positive characteristic, or any homomorphism factorizing through a regular local ring) and of finite Gorenstein dimension relative to \(C\), then \(C\) is dualizing.