Quick Search:

uzh logo
Browse by:
bullet
bullet
bullet
bullet

Zurich Open Repository and Archive 

Brodmann, M; Rotthaus, C; Sharp, R (2000). On annihilators and associated primes of local cohomology modules. Journal of Pure and Applied Algebra, 153(3):197-227.

Full text not available from this repository.

Abstract

We establish the Local-global Principle for the annihilation of local cohomology modules over an arbitrary commutative Noetherian ring R at level 2. We also establish the same principle at all levels over an arbitrary commutative Noetherian ring of dimension not exceeding 4. We explore interrelations between the principle and the Annihilator Theorem for local cohomology, and show that, if R is universally catenary and all formal fibres of all localizations of R satisfy Serre's condition (Sr), then the Annihilator Theorem for local cohomology holds at level r over R if and only if the Local-global Principle for the annihilation of local cohomology modules holds at level r over R. Moreover, we show that certain local cohomology modules have only finitely many associated primes. This provides motivation for the study of conditions under which the set Um,n∈ℕ Ass(M/(Xm,yn)M) (where M is a finitely generated R-module and x, y ∈ R) is finite: an example due to M. Katzman shows that this set is not always finite; we provide some sufficient conditions for its finiteness. © 2000 Elsevier Science B.V. All rights reserved.

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
DDC:510 Mathematics
Uncontrolled Keywords:local cohomology module; finiteness dimension; local-global principle
Language:English
Date:2000
Deposited On:31 May 2010 15:34
Last Modified:27 Nov 2013 23:14
Publisher:Elsevier
ISSN:0022-4049
Publisher DOI:10.1016/S0022-4049(99)00104-8
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0968.13010
http://www.ams.org/mathscinet-getitem?mr=1783166
Citations:Web of Science®. Times Cited: 32
Google Scholar™
Scopus®. Citation Count: 26

Users (please log in): suggest update or correction for this item

Repository Staff Only: item control page