Asymptotic stability of certain sets of associated prime ideals of local cohomology modules

Details Asymptotic stability of certain sets of associated prime ideals of local cohomology modules Asymptotic stability of certain sets of associated prime ideals of local cohomology modules

2008-04-07

arxiv.org/abs/0804.0964v1

Mathematics

Commutative Algebra

13 pages

Scientific paper

Let $(R,\m)$ be a Noetherian local ring $I, J$ two ideals of $R$ and $M$ a finitely generated $R-$module. It is first shown that for $k\geq -1$ the integer $r_k = \depth_k(I,J^nM/J^{n+1}M)$, it is the length of a maximal $(J^nM/J^{n+1}M)-$sequence in dimension $>k$ in $I$ defined by M. Brodmann and L. T. Nhan \cite{BN}, becomes for large $n$ independent of $n$. Then we prove in this paper that the sets $\bigcup_{j\le r_k}\Ass_R(H^j_I(J^nM/J^{n+1}M))$ with $k=-1$ or $k=0$, and $\bigcup_{j\le r_1}\Ass_R(H^j_I(J^nM/J^{n+1}M))\cup\{\m\}$ are stable for large $n$. We also obtain similar results for modules $M/J^nM$.

Affiliated with

Also associated with

No associations

Rating

Asymptotic stability of certain sets of associated prime ideals of local cohomology modules 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 Asymptotic stability of certain sets of associated prime ideals of local cohomology modules, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Asymptotic stability of certain sets of associated prime ideals of local cohomology modules will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-729846