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It is shown that the $R$-module $\\Ext^i_R(R/I,M)$ is finitely generated (resp. weakly Laskerian) for all $i\\leq {\\rm cd}(I,M)+1$ if and only if the local cohomology module $H^i_I(M)$ is $I$-cofinite (resp. $I$-weakly cofinite) for all $i$. Also, we show that when $I$ is an arbitrary ideal and $M$ is finitely generated module such that the $R$-module $H^i_I(M)$ is weakly Laskerian for all $i\\leq t-1$, then $H^i_I(M)$ is $I$-cofinite for all $i\\leq t-1$ and "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1308.6040","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-08-28T03:05:35Z","cross_cats_sorted":[],"title_canon_sha256":"981ef87e38bae5fac61a93c58d79f341baa130492d628252610785a0e0d7c222","abstract_canon_sha256":"35c9b0a5fdc92948051a1797da7ca928b1f7ee57427c995833c6ab78a886f107"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:49.253415Z","signature_b64":"AHMQ/Z88sIH6teRgeYp0JP7vWPSxefyCNecnVyaGbAhTde8Vh86lCARSNdF3lmfV31T5m3O7asuNXvunD7MNDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55b48d001e4555ec75cbdd6ec40d36ef9be66b3c72688cff4fc821b6c74a3e54","last_reissued_at":"2026-05-18T03:14:49.252772Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:49.252772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cofiniteness of local cohomology modules for ideals of dimension one","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Kamal Bahmanpour, Monireh Sedghi, Reza Naghipour","submitted_at":"2013-08-28T03:05:35Z","abstract_excerpt":"Let $R$ denote a commutative Noetherian (not necessarily local) ring, $M$ an arbitrary $R$-module and $I$ an ideal of $R$ of dimension one. It is shown that the $R$-module $\\Ext^i_R(R/I,M)$ is finitely generated (resp. weakly Laskerian) for all $i\\leq {\\rm cd}(I,M)+1$ if and only if the local cohomology module $H^i_I(M)$ is $I$-cofinite (resp. $I$-weakly cofinite) for all $i$. 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