{"paper":{"title":"A New Outlook on Cofiniteness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Hossein Faridian, Kamran Divaani-Aazar, Massoud Tousi","submitted_at":"2017-01-26T14:30:35Z","abstract_excerpt":"Let $\\mathfrak{a}$ be an ideal of a commutative noetherian (not necessarily local) ring $R$. In the case $\\cd(\\mathfrak{a},R)\\leq 1$, we show that the subcategory of $\\mathfrak{a}$-cofinite $R$-modules is abelian. Using this and the technique of way-out functors, we show that if $\\cd(\\mathfrak{a},R)\\leq 1$, or $\\dim(R/\\mathfrak{a}) \\leq 1$, or $\\dim(R) \\leq 2$, then the local cohomology module $H^{i}_{\\mathfrak{a}}(X)$ is $\\mathfrak{a}$-cofinite for every $R$-complex $X$ with finitely generated homology modules and every $i \\in \\mathbb{Z}$. We further answer Question 1.3 in the three aforement"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07716","kind":"arxiv","version":3},"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"}