Cofiniteness and associated primes of local cohomology modules

Details Cofiniteness and associated primes of local cohomology modules Cofiniteness and associated primes of local cohomology modules

2002-09-17

arxiv.org/abs/math/0209216v1

Journal of Algebra 256 (2002), 180-193

Mathematics

Commutative Algebra

12 pages; accepted May 2002 for publication in Journal of Algebra

Scientific paper

Let R be a regular local ring of dimension d, I an ideal of R, and M a finitely generated R-module of dimension n. We prove that the set of associated primes of Ext^i_R(R/I,H^j_I(M)) is finite for all i and j in the following cases: (1) dim M\le 3; (2) dim R\le 4; (3) dim M/IM \le 2 and M satisfies Serre's condition S_{n-3}; (4) dim M/IM\le 3, R is unramified, and M is faithful and satisfies S_{n-3}. We also prove that if dim R/I\ge 2 and the punctured spectrum of R/I is disconnected then H^{d-1}_I(R) is not I-cofinite. This generalizes a result due to Huneke and Koh.

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