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Supporting degrees of multi-graded local cohomology modules


Brodmann, M; Sharp, R Y (2009). Supporting degrees of multi-graded local cohomology modules. Journal of Algebra, 321(2):450-482.

Abstract

For a finitely generated graded module M over a positively-graded commutative Noetherian ring R, the second author established in 1999 some restrictions, which can be formulated in terms of the Castelnuovo regularity of M or the so-called a*-invariant of M, on the supporting degrees of a graded-indecomposable graded-injective direct summand, with associated prime ideal containing the irrelevant ideal of R, of any term in the minimal graded-injective resolution of M. Earlier, in 1995, T. Marley had established connections between finitely graded local cohomology modules of M and local behaviour of M across Proj(R).

The purpose of this paper is to present some multi-graded analogues of the above-mentioned work.

Abstract

For a finitely generated graded module M over a positively-graded commutative Noetherian ring R, the second author established in 1999 some restrictions, which can be formulated in terms of the Castelnuovo regularity of M or the so-called a*-invariant of M, on the supporting degrees of a graded-indecomposable graded-injective direct summand, with associated prime ideal containing the irrelevant ideal of R, of any term in the minimal graded-injective resolution of M. Earlier, in 1995, T. Marley had established connections between finitely graded local cohomology modules of M and local behaviour of M across Proj(R).

The purpose of this paper is to present some multi-graded analogues of the above-mentioned work.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2009
Deposited On:11 Nov 2009 15:01
Last Modified:05 Apr 2016 13:31
Publisher:Elsevier
ISSN:0021-8693
Publisher DOI:https://doi.org/10.1016/j.jalgebra.2008.10.013
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2483276
http://arxiv.org/abs/0810.4487

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