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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
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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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