Recognizing dualizing complexes
Volume 176 / 2003
Fundamenta Mathematicae 176 (2003), 251-259
MSC: 13D25, 16E45.
DOI: 10.4064/fm176-3-4
Abstract
Let $A$ be a noetherian local commutative ring and let $M$ be a suitable complex of $A$-modules. It is proved that $M$ is a dualizing complex for $A$ if and only if the trivial extension $A \ltimes M$ is a Gorenstein differential graded algebra. As a corollary, $A$ has a dualizing complex if and only if it is a quotient of a Gorenstein local differential graded algebra.
