## “School of Mathematics”

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Paper   IPM / M / 729
School of Mathematics
Title:   The Lichtenbaum-Hartshorne theorem for generalized local cohomology and connectedness
Author(s):
 1 R. Naghipour 2 K. Divaani-Aazar 3 M. Tousi
Status:   Published
Journal: Comm. Algebra
No.:  8
Vol.:  30
Year:  2002
Pages:   3687-3702
Supported by:  IPM
Abstract:
Let Z be a subset of the spectrum of a local ring R stable under specialization and let N be a d-dimensional finitely generated R-module. It is shown that HZd(N), the d-th local cohomology module of the sheaf associated to N with support in Z, vanishes if and only if for every d-dimensional \fp ∈ \TAssR N, there is a \fq ∈ Z such that dimR/(\fqR+\fp) > 0. Applying this criterion for vanishing of HZd (N), several connectedness results for certain algebraic varieties are proved.

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