Asymptotic stability of certain sets of associated prime ideals of local cohomology modules

2008/04/07 by Nguyen Tu Cuong, Cuong, Nguyen Tu, Nguyễn Văn Minh Hoàng +3
Mathematics · #13D45 #13E05 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.0804.0964

openalex publication_date 2008/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (R,\m) be a Noetherian local ring I, J two ideals of R and M a finitely generated R-module. It is first shown that for k≥ -1 the integer r_k = \depth_k(I,JⁿM/Jⁿ⁺¹M), it is the length of a maximal (JⁿM/Jⁿ⁺¹M)-sequence in dimension >k in I defined by M. Brodmann and L. T. Nhan \citeBN, becomes for large n independent of n. Then we prove in this paper that the sets \bigcup_{j≤ rk}\Ass_R(H^j_I(JⁿM/Jⁿ⁺¹M)) with k=-1 or k=0, and \bigcup_{j≤ r1}\Ass_R(H^j_I(JⁿM/Jⁿ⁺¹M))∪\\m\ are stable for large n. We also obtain similar results for modules M/JⁿM.

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