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A test complex for Gorensteinness

Lars Winther Christensen·Oana Veliche
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Abstract

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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Lars Winther Christensen, Oana Veliche. 2007-01-17. A test complex for Gorensteinness. https://arxiv.org/abs/math/0607355

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