On the Set of Associated Primes of a Local Cohomology Module

By M. Hellus. 2001

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Abstract 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  ∈  R and Ass R ( H 3 ( x 1 ,  x 2 ,  y ) ( R )) is finite for any y  ∈  R and any regular sequence x 1 , x 2  ∈  R . Furthermore it is shown that Ass R ( H l I ( R )) is always finite if dim( R ) ≤ 3. The same statement is even true for dim( R ) ≤ 4 if R is almost factorial.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/2066e45880aa7c26e3bf47c8abf67f73c775d6ef