Generalized local cohomology modules and homological Gorenstein dimensions

Details Generalized local cohomology modules and homological Gorenstein dimensions Generalized local cohomology modules and homological Gorenstein dimensions

2008-03-02

arxiv.org/abs/0803.0107v3

Mathematics

Commutative Algebra

Corollary 3.6 is slightly changed. This version has 17 pages and it will be published in Communications in Algebra

Scientific paper

Let \fa be an ideal of a commutative Noetherian ring R and M and N two finitely generated R-modules. Let \cd_{\fa}(M,N) denote the supremum of the i's such that H^i_{\fa}(M,N)\neq 0. First, by using the theory of Gorenstein homological dimensions, we obtain several upper bounds for \cd_{\fa}(M,N). Next, over a Cohen-Macaulay local ring (R,\fm), we show that \cd_{\fm}(M,N)=\dim R-\grade(\Ann_RN,M), provided that either projective dimension of M or injective dimension of N is finite. Finally, over such rings, we establish an analogue of the Hartshorne-Lichtenbaum Vanishing Theorem in the context of generalized local cohomology modules.

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