Graded annihilators of modules over the Frobenius skew polynomial ring, and tight closure

Details Graded annihilators of modules over the Frobenius skew polynomial ring, and tight closure Graded annihilators of modules over the Frobenius skew polynomial ring, and tight closure

2006-05-12

arxiv.org/abs/math/0605329v1

Mathematics

Commutative Algebra

This is to appear in the Transactions of the American Mathematical Society

Scientific paper

This paper is concerned with the tight closure of an ideal in a commutative Noetherian local ring $R$ of prime characteristic $p$. Several authors, including R. Fedder, K.-i. Watanabe, K. E. Smith, N. Hara and F. Enescu, have used the natural Frobenius action on the top local cohomology module of such an $R$ to good effect in the study of tight closure, and this paper uses that device. The main part of the paper develops a theory of what are here called 'special annihilator submodules' of a left module over the Frobenius skew polynomial ring associated to $R$; this theory is then applied in the later sections of the paper to the top local cohomology module of $R$ and used to show that, if $R$ is Cohen--Macaulay, then it must have a weak parameter test element, even if it is not excellent.

Affiliated with

Also associated with

No associations

Rating

Graded annihilators of modules over the Frobenius skew polynomial ring, and tight closure 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 Graded annihilators of modules over the Frobenius skew polynomial ring, and tight closure, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Graded annihilators of modules over the Frobenius skew polynomial ring, and tight closure will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-596597