A test complex for Gorensteinness
arXiv:math/0607355
Abstract
Let 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 is from being Gorenstein. In particular, 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 is Gorenstein.
Final version, 8 pp. To appear in Proc. Amer. Math. Soc. Also available from the authors' homepages at http://www.math.unl.edu/~lchristensen3/ and at http://www.math.utah.edu/~oveliche/