A test complex for Gorensteinness
Authors:
Lars Winther Christensen and Oana Veliche
Journal:
Proc. Amer. Math. Soc. 136 (2008), 479-487
MSC (2000):
Primary 13H10, 13D25
DOI:
https://doi.org/10.1090/S0002-9939-07-09129-0
Published electronically:
November 6, 2007
MathSciNet review:
2358487
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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.
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Additional Information
Lars Winther Christensen
Affiliation:
Department of Mathematics, University of Nebraska, Lincoln, Nebraska 68588
Address at time of publication:
Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas 79409
MR Author ID:
671759
ORCID:
0000-0002-9360-123X
Email:
winther@math.unl.edu, lars.w.christensen@ttu.edu
Oana Veliche
Affiliation:
Department of Mathematics, University of Utah, Salt Lake City, Utah 84112
Email:
oveliche@math.utah.edu
Keywords:
Gorenstein rings,
dualizing complexes,
totally acyclic complexes
Received by editor(s):
July 14, 2006
Received by editor(s) in revised form:
December 6, 2006, and January 17, 2007
Published electronically:
November 6, 2007
Additional Notes:
The first author was partly supported by a grant from the Carlsberg Foundation.
Communicated by:
Bernd Ulrich
Article copyright:
© Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
