Recognizing dualizing complexes

Details Recognizing dualizing complexes Recognizing dualizing complexes

2003-03-09

arxiv.org/abs/math/0303105v1

Mathematics

Commutative Algebra

9 pages. To appear in Fundamenta Mathematicae

Scientific paper

Let A be a noetherian local commutative ring and let M be a suitable complex
of A-modules. This paper proves 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 follows that A has a dualizing complex if and only if
it is a quotient of a Gorenstein local Differential Graded Algebra.

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