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A test complex for Gorensteinness
Author(s):
Lars
Winther
Christensen;
Oana
Veliche
Journal:
Proc. Amer. Math. Soc.
136
(2008),
479-487.
MSC (2000):
Primary 13H10, 13D25
Posted:
November 6, 2007
MathSciNet review:
2358487
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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.
References:
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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:
10.1090/S0002-9939-07-09129-0
PII:
S 0002-9939(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
Posted:
November 6, 2007
Additional Notes:
The first author was partly supported by a grant from the Carlsberg Foundation.
Communicated by:
Bernd Ulrich
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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