Asymptotic Stability of Certain Sets of Associated Prime Ideals of Local Cohomology Modules

摘要

Let (R, ) 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~nM/J~(n+1)M) be the length of a maximal (J~nM/J~(n+1)M)-sequence in dimension >k in I defined by Brodmann and Nhan [4]. It is first shown that r_k becomes independent of n for large n. Then we prove in this article that the sets _(j≤rk) Ass_R (H~j_I (J~n M/J~(n+1) M) with k = -1 or k = 0, and U_(j≤r1) Ass_R (H~j_I (J~n M/J~(n+1) M) U {m} are stable for large n. We also obtain similar results for modules M/J~nM.