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A duality theorem for generalized local cohomology
Author(s):
Marc
Chardin;
Kamran
Divaani-Aazar
Journal:
Proc. Amer. Math. Soc.
136
(2008),
2749-2754.
MSC (2000):
Primary 13D45, 14B15, 13D07, 13C14
Posted:
February 28, 2008
MathSciNet review:
2399038
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Abstract:
We prove a duality theorem for graded algebras over a field that implies several known duality results: graded local duality, versions of Serre duality for local cohomology and of Suzuki duality for generalized local cohomology, and Herzog-Rahimi bigraded duality.
References:
-
- [B]
- N. Bourbaki, Algèbre, Chapitre X, Herman, Paris, 1980.
- [CCHS]
- M. Chardin, S. D. Cutkosky, J. Herzog and H. Srinivasan, Duality and Tameness, arXiv:0704.0102v1 (to appear in Michigan Math. J.).
- [CD]
- M. Chardin and K. Divaani-Aazar, Generalized local cohomology and regularity of Ext modules, arXiv:math/0701509 (to appear in J. Algebra).
- [H]
- J. Herzog, Komplex Auflösungen und Dualität in der lokalen algebra, preprint, Universitüt Regensburg, 1974.
- [HR]
- J. Herzog and A. Rahimi, Local Duality for Bigraded Modules, math.AC/0604587.
- [S]
- N. Suzuki, On the generalized local cohomology and its duality, J. Math. Kyoto. Univ. 18 (1) (1978), 71-85. MR 490835 (80i:13004)
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Additional Information:
Marc
Chardin
Affiliation:
C.N.R.S., Institut de Mathématiques de Jussieu, 175 rue du Chevaleret, F-75013, Paris, France
Email:
chardin@math.jussieu.fr
Kamran
Divaani-Aazar
Affiliation:
Department of Mathematics, Az-Zahra University, Vanak, Post Code 19834, Tehran, Iran
Email:
kdivaani@ipm.ir
DOI:
10.1090/S0002-9939-08-09400-8
PII:
S 0002-9939(08)09400-8
Keywords:
Generalized local cohomology,
duality.
Received by editor(s):
May 21, 2007
Received by editor(s) in revised form:
September 13, 2007
Posted:
February 28, 2008
Communicated by:
Bernd Ulrich
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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