The associated primes of local cohomology modules over rings of small dimension |
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Authors: | Thomas Marley |
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Affiliation: | (1) Department of Mathematics and Statistics, University of Nebraska-Lincoln, Lincoln, NE 68588-0323, USA. e mail: tmarley@math.unl.edu, US |
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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. Received: 31 October 2000 / Revised version: 8 January 2001 |
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Keywords: | Mathematics Subject Classification (2000): Primary 13D45 |
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