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 
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 
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.
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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
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
DOI:
https://doi.org/10.1090/S0002-9939-07-09129-0
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.
