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arXiv · 1702.02986

Totally acyclic complexes and locally Gorenstein rings

Lars Winther Christensen·Kiriko Kato
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Abstract

A commutative noetherian ring with a dualizing complex is Gorenstein if and only if every acyclic complex of injective modules is totally acyclic. We extend this characterization, which is due to Iyengar and Krause, to arbitrary commutative noetherian rings, i.e. we remove the assumption about a dualizing complex. In this context Gorenstein, of course, means locally Gorenstein at every prime.

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Lars Winther Christensen, Kiriko Kato. 2017-02-09. Totally acyclic complexes and locally Gorenstein rings. https://arxiv.org/abs/1702.02986

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