Abstract
Abstract Let C be a semidualizing complex over a noetherian local ring A. If there exists a local homomorphism A → B ${A \rightarrow B}$ 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.
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