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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"},"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":"1701.07716","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-01-26T14:30:35Z","cross_cats_sorted":[],"title_canon_sha256":"eee049003a3fdddb3d406a48888f8bf3eb65a5d9249abe1850b42710e4f9f06a","abstract_canon_sha256":"5ac3a3c4d88a8b1c2b5535569630547bf5c632876834c017004587167fd7fa58"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:27.291704Z","signature_b64":"OTJuod4vqfIWOL/3bmDxJ75M7YeGQeOOLVL3fqjvxxcXVV8QTNCvtJ9kdNR3hVtsiqYpfI4+uCZMqnwzd2ZRBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51a63984a0e21e778c954064163eca2d22ca8d3b615a850a54af84974d2a3d1c","last_reissued_at":"2026-05-18T00:17:27.291112Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:27.291112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $R$. 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