{"paper":{"title":"On the finiteness and stability of certain sets of associated primes ideals of local cohomology modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Nguyen Tu Cuong, Nguyen Van Hoang","submitted_at":"2012-11-07T07:58:43Z","abstract_excerpt":"Let $(R,\\frak{m})$ be a Noetherian local ring, $I$ an ideal of $R$ and $N$ a finitely generated $R$-module. Let $k{\\ge}-1$ be an integer and $ r=\\depth_k(I,N)$ the length of a maximal $N$-sequence in dimension $>k$ in $I$ defined by M. Brodmann and L. T. Nhan ({Comm. Algebra, 36 (2008), 1527-1536). For a subset $S\\subseteq \\Spec R$ we set $S_{{\\ge}k}={\\p\\in S\\mid\\dim(R/\\p){\\ge}k}$. We first prove in this paper that $\\Ass_R(H^j_I(N))_{\\ge k}$ is a finite set for all $j{\\le}r$}. Let $\\fN=\\oplus_{n\\ge 0}N_n$ be a finitely generated graded $\\fR$-module, where $\\fR$ is a finitely generated standard"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1477","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}