Vanishing of the top local cohomology modules over Noetherian rings

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dc.creatorDivaani-Aazar, Kamran
dc.date2007-02-06
dc.date.accessioned2026-07-07T07:45:06Z
dc.date.available2026-07-07T07:45:06Z
dc.descriptionLet R be a (not necessarily local) Noetherian ring and M a finitely generated R-module of finite dimension d. Let \fa be an ideal of R and \fM denote the intersection of all prime ideals \fp in Supp_RH^d_{\fa}(M). It is shown that H^d_{\fa}(M)\simeq H^d_{\fM}(M)/\displaystyle{\sum_{n\in \mathbb{N}}}<\fM>(0:_{H^d_{\fM}(M)}\fa^n), where for an Artinian R-module A we put <\fM>A=\cap_{n\in \mathbb{N}} \fM^nA. As a consequence, it is proved that for all ideals \fa of R, there are only finitely many non-isomorphic top local cohomology modules H^d_{\fa}(M) having the same support. In addition, we establish an analogue of the Lichtenbaum-Hartshorne Vanishing Theorem over rings that need not be local.
dc.description14 pages
dc.identifierhttps://arxiv.org/abs/math/0702159
dc.identifierhttp://arxiv.org/abs/math/0702159
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/123429
dc.subjectCommutative Algebra
dc.subject13D45, 13E10
dc.titleVanishing of the top local cohomology modules over Noetherian rings
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