On the Set of Associated Primes of a Local Cohomology Module

Abstract

Assume R is a local Cohen–Macaulay ring. It is shown that AssR(HlI(R)) is finite for any ideal I and any integer l provided AssR(H2(x,y)(R)) is finite for any x, y∈R and AssR(H3(x1,x2,y)(R)) is finite for any y∈R and any regular sequence x1, x2∈R. Furthermore it is shown that AssR(HlI(R)) is always finite if dim(R)≤3. The same statement is even true for dim(R)≤4 if R is almost factorial.