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 ⋉ 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm176-3-4,
author = {Peter J\o rgensen},
title = {Recognizing dualizing complexes},
journal = {Fundamenta Mathematicae},
volume = {177},
year = {2003},
pages = {251-259},
zbl = {1019.13007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm176-3-4}
}
Peter Jørgensen. Recognizing dualizing complexes. Fundamenta Mathematicae, Tome 177 (2003) pp. 251-259. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm176-3-4/