Vanishing of the top local cohomology modules over Noetherian rings

Details Vanishing of the top local cohomology modules over Noetherian rings Vanishing of the top local cohomology modules over Noetherian rings

2007-02-06

arxiv.org/abs/math/0702159v1

Mathematics

Commutative Algebra

14 pages

Scientific paper

Let 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.

Affiliated with

Also associated with

No associations

Rating

Vanishing of the top local cohomology modules over Noetherian rings does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Vanishing of the top local cohomology modules over Noetherian rings, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Vanishing of the top local cohomology modules over Noetherian rings will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-427444