On the set of associated primes of a local cohomology module

Details On the set of associated primes of a local cohomology module On the set of associated primes of a local cohomology module

2006-07-04

arxiv.org/abs/math/0607075v1

J. Algebra 237, (2001) 406-419

Mathematics

Commutative Algebra

14 pages

Scientific paper

Assume $R$ is a local Cohen-Macaulay ring. It is shown that $\Ass_R (H^l_I(R))$ is finite for any ideal $I$ and any integer $l$ provided $\Ass_R (H^2_{(x,y)}(R))$ is finite for any $x,y\in R$ and $\Ass_R (H^3_{(x_1,x_2,y)}(R))$ is finite for any $y\in R$ and any regular sequence $x_1,x_2\in R$. Furthermore it is shown that $\Ass_R (H^l_I(R))$ is always finite if $\dim (R)\leq 3$. The same statement is even true for $\dim (R)\leq 4$ if $R$ is almost factorial.

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