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COMPARISON OF MULTIGRADED AND UNGRADED COUSIN COMPLEXES

Published online by Cambridge University Press:  20 January 2009

M. H. Dogani Aghcheghloo ,
R. Enshaei ,
S. Goto  and
R. Y. Sharp
M. H. Dogani Aghcheghloo
Affiliation:
Department of Pure Mathematics, Faculty of Mathematics, The University of Shahid Bahonar (Kerman), Kerman, Iran ([email protected])
R. Enshaei
Affiliation:
Department of Mathematics, University of Isfahan, Isfahan 81744, Iran ([email protected])
S. Goto
Affiliation:
Department of Mathematics, School of Science and Technology, Meiji University, Higashi-mita 1-1-1, Tama-ku, Kawasaki-shi 214-8571, Japan ([email protected])
R. Y. Sharp
Affiliation:
Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH, UK ([email protected])
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Abstract

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This paper generalizes, in two senses, work of Petzl and Sharp, who showed that, for a $\mathbb{Z}$-graded module $M$ over a $\mathbb{Z}$-graded commutative Noetherian ring $R$, the graded Cousin complex for $M$ introduced by Goto and Watanabe can be regarded as a subcomplex of the ordinary Cousin complex studied by Sharp, and that the resulting quotient complex is always exact. The generalizations considered in this paper are, firstly, to multigraded situations and, secondly, to Cousin complexes with respect to more general filtrations than the basic ones considered by Petzl and Sharp. New arguments are presented to provide a sufficient condition for the exactness of the quotient complex in this generality, as the arguments of Petzl and Sharp will not work for this situation without additional input.

AMS 2000 Mathematics subject classification: Primary 13A02; 13E05; 13D25; 13D45

Keywords

$\mathbb{Z}^n$-graded commutative Noetherian ringCousin complexlocal cohomology modules
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 44 , Issue 2 , June 2001 , pp. 365 - 378
Copyright
Copyright © Edinburgh Mathematical Society 2001