A test complex for gorensteinness

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Abstract

Let R be a commutative noetherian ring with a dualizing complex. By recent work of Iyengar and Krause (2006), 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.

Original languageEnglish
Pages (from-to)479-487
Number of pages9
JournalProceedings of the American Mathematical Society
Volume136
Issue number2
DOIs
StatePublished - Feb 2008

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