ASYMPTOTIC STABILITY OF CERTAIN SETS OF ASSOCIATED PRIME IDEALS OF LOCAL COHOMOLOGY MODULES

Let (R, m) be a Noetherian local ring I, J two ideals of R and M a finitely generated R-module. Let k >= -1 and r(k) = depth(k) (I, J(n)M/J(n+1)M) be the length of a maximal (J(n)M/J(n+1)M)-sequence in dimension > k in I defined by Brodmann and Nhan [4]. It is first shown that rk becomes independent of n for large n. Then we prove in this article that the sets U-j <= rk Ass(R) (H-I(j) (J(n)M/J(n+1)M)) with k = -1 or k = 0, and U-j <= r1 Ass(R) (H-I(j) (J(n)M/J(n+1)M))U {m} are stable for large n. We also obtain similar results for modules M/J(n)M.