Generalized Local Cohomology Modules and Homological Gorenstein Dimensions.

Let  be an ideal of a commutative Noetherian ring R and M and N two finitely generated R-modules. Let cd(M, N) denote the supremum of the i's such that [image omitted]. First, by using the theory of Gorenstein homological dimensions, we obtain several upper bounds for cd(M, N). Next, over a Cohen-Macaulay local ring (R, ), we show that [image omitted] 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. [ABSTRACT FROM AUTHOR]