A test complex for Gorensteinness

Details A test complex for Gorensteinness A test complex for Gorensteinness

2006-07-14

arxiv.org/abs/math/0607355v2

Mathematics

Commutative Algebra

Final version, 8 pp. To appear in Proc. Amer. Math. Soc. Also available from the authors' homepages at http://www.math.unl.e

Scientific paper

Let $R$ be a commutative noetherian ring with a dualizing complex. By recent work of Iyengar and Krause, the difference between the category of acyclic complexes and its subcategory of totally acyclic complexes measures how far $R$ is from being Gorenstein. In particular, $R$ is Gorenstein if and only if every acyclic complex is totally acyclic. In this note we exhibit a specific acyclic complex with the property that it is totally acyclic if and only if $R$ is Gorenstein.

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