English

Associated primes of local cohomology module

Commutative Algebra 2016-09-07 v1

Abstract

Let \fa\fa be an ideal of a commutative Noetherian ring RR and MM a finitely generated RR-module. Let tt be a natural integer. It is shown that there is a finite subset XX of \SpecR\Spec R, such that \AssR(H\fat(M))\Ass_R(H_{\fa}^t(M)) is contained in XX union with the union of the sets \AssR(\ExtRj(R/\fa,H\fai(M)))\Ass_R(\Ext_R^j(R/\fa,H_{\fa}^i(M))), where 0i<t0\leq i<t and 0jt2+10\leq j\leq t^2+1. As an immediate consequence, we deduce that the first non \fa\fa-cofinite local cohomology module of MM with respect to \fa\fa has only finitely many associated prime ideals.

Keywords

Cite

@article{arxiv.math/0410598,
  title  = {Associated primes of local cohomology module},
  author = {Kamran Divaani-Aazar and Amir Mafi},
  journal= {arXiv preprint arXiv:math/0410598},
  year   = {2016}
}

Comments

7 pages, to appear in Proceedings of the American Mathematical Society