{"paper":{"title":"Weakly cofiniteness of local cohomology modules","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Moharram Aghapournahr","submitted_at":"2017-07-21T08:32:10Z","abstract_excerpt":"Let $R$ be a commutative Noetherian ring, $\\Phi$ a system of ideals of $R$ and $I\\in \\Phi$. Let $M$ be an $R$-module (not necessary $I$-torsion) such that $\\dim M\\leq 1$, then the $R$-module $\\Ext^i_{R}(R/I, M)$ is weakly Laskerian, for all $i\\geq 0$, if and only if the $R$-module $\\Ext^i_{R}(R/I, M)$ is weakly Laskerian, for $i=0, 1$. Let $t\\in\\Bbb{N}_0$ be an integer and $M$ an $R$-module such that $\\Ext^i_R(R/I,M)$ is weakly Laskerian for all $i\\leq t+1$. We prove that if the $R$-module $\\lc^{i}_\\Phi(M)$ is ${\\rm FD_{\\leq 1}}$ for all $i<t$, then $\\lc^{i}_\\Phi(M)$ is $\\Phi$-weakly cofinite "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06795","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"}