Abstract:
Let R be a commutative Noetherian local ring of dimension d, I an ideal of R, and M a finitely generated R-module. We prove that the set of associated primes of the local cohomology module H i I (M) is finite for all i≥ 0 in the following cases: (1) d≤ 3; (2) d= 4 and $R$ is regular on the punctured spectrum; (3) d= 5, R is an unramified regular local ring, and M is torsion-free. In addition, if $d>0$ then H d − 1 I (M) has finite support for arbitrary R, I, and M.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 31 October 2000 / Revised version: 8 January 2001
Rights and permissions
About this article
Cite this article
Marley, T. The associated primes of local cohomology modules over rings of small dimension. manuscripta math. 104, 519–525 (2001). https://doi.org/10.1007/s002290170024
Issue Date:
DOI: https://doi.org/10.1007/s002290170024