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arXiv · 0803.0107

Generalized local cohomology modules and homological Gorenstein dimensions

Kamran Divaani-Aazar·Alireza Hajikarimi
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Abstract

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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Kamran Divaani-Aazar, Alireza Hajikarimi. 2010-08-05. Generalized local cohomology modules and homological Gorenstein dimensions. https://arxiv.org/abs/0803.0107

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