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Then for each finitely generated $S$-module $N$ with $\\Supp N=V(aS)$ the socle of $H^2_{(u,v)S}(N)$ is infinite dimensional. Also, using this result, for any commutative Noetherian complete local ring $(R,\\m)$, we characterize the class of all ideals $I$ of $R$ with the property that, for every finitely generated $R$-module $M$, the local cohomology modules $H^i_I(M)$ are $I$-cofinit"},"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":"1901.06668","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-01-20T12:29:33Z","cross_cats_sorted":[],"title_canon_sha256":"2ccc0ddc60c6de48978e6527918296bdc72b8725ef2342fbe3c3fa462939b04b","abstract_canon_sha256":"1d08db8ecf48a28e5d20200ec672ac0ef206f42308dd9461b589c94c60321c03"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:49.512415Z","signature_b64":"igKnTyEo6XvGxK5aS9qeK+xTp9gEOP547JGerYKCWQgc2MR2IiQDZNE4o/Lal3mNBghNifblE46UWqCTrMmlCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d4131dd03a5ed61e2781e64dcf4553f313ff708711b71dce47c8acd6e105261","last_reissued_at":"2026-05-17T23:55:49.511709Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:49.511709Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cofiniteness over Noetherian complete local rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Bahmanpour, Kamal","submitted_at":"2019-01-20T12:29:33Z","abstract_excerpt":"In this paper we prove the following generalization of a result of Hartshorne: Let $(S,\\n)$ be a regular local ring of dimension $4$. 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