{"paper":{"title":"A note on Abelian categories of cofinite modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Bahmanpour, Kamal","submitted_at":"2019-01-20T12:36:53Z","abstract_excerpt":"Let $R$ be a commutative Noetherian ring and $I$ be an ideal of $R$. In this article we answer affirmatively a question raised by the present author in \\cite{B2}. Also, as an immediate consequence of this result it is shown that the category of all $I$-cofinite $R$-modules $\\mathscr{C}(R, I)_{cof}$ is an Abelian subcategory of the category of all $R$-modules, whenever $q(I,R)\\leq 1$. These assertions answer affirmatively a question raised by R. Hartshorne in [{\\it Affine duality and cofiniteness}, Invent. Math. {\\bf9}(1970), 145-164], in some special cases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.06671","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"}