Recognizing dualizing complexes
Abstract
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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- March 2003
- DOI:
- arXiv:
- arXiv:math/0303105
- Bibcode:
- 2003math......3105J
- Keywords:
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- Commutative Algebra;
- Rings and Algebras;
- Representation Theory;
- 13D25;
- 16E45
- E-Print:
- 9 pages. To appear in Fundamenta Mathematicae