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Let $M$ be an $R$-module (not necessary $I$-torsion) such that $\\dim M\\leq 1$, then the $R$-module $\\Ext^i_{R}(R/I, M)$ is weakly Laskerian, for all $i\\geq 0$, if and only if the $R$-module $\\Ext^i_{R}(R/I, M)$ is weakly Laskerian, for $i=0, 1$. Let $t\\in\\Bbb{N}_0$ be an integer and $M$ an $R$-module such that $\\Ext^i_R(R/I,M)$ is weakly Laskerian for all $i\\leq t+1$. We prove that if the $R$-module $\\lc^{i}_\\Phi(M)$ is ${\\rm FD_{\\leq 1}}$ for all $i<t$, then $\\lc^{i}_\\Phi(M)$ is $\\Phi$-weakly cofinite ","authors_text":"Moharram Aghapournahr","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AC","submitted_at":"2017-07-21T08:32:10Z","title":"Weakly cofiniteness of local cohomology modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06795","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2b01acc24ec99cb634e5b9f6df74841854b547fe4e9119e5871de61dcab44077","target":"record","created_at":"2026-05-18T00:39:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"5202275c7cb30ad4f4e4bee17838420385b91c0135615ff43c66ee22126ef0cd","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AC","submitted_at":"2017-07-21T08:32:10Z","title_canon_sha256":"8b7e9a0705cdc2883fdeaf3aa4071171e056120f9467459ef9390dc84ab34982"},"schema_version":"1.0","source":{"id":"1707.06795","kind":"arxiv","version":1}},"canonical_sha256":"59b8b8a4338de3c74944c985e86895bc392f5d7eb56a63b5db5512595eec581b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59b8b8a4338de3c74944c985e86895bc392f5d7eb56a63b5db5512595eec581b","first_computed_at":"2026-05-18T00:39:51.619379Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:51.619379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wdJuNFv+kupDe278PTKLBQ8UlaXiY5BLsS7SVuATR43fE7oWtNyidtBdndfrMqdPDMVs4G3HinyqOmrJlZQOAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:51.619868Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.06795","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b01acc24ec99cb634e5b9f6df74841854b547fe4e9119e5871de61dcab44077","sha256:3d53d53a061f4bd56a21817062a80a65c526e03eed525b9a65dfe41ed2d4af7c"],"state_sha256":"f9784d23de7efc2a85e4bd410dbcb5d8b426c22c486418d166f77eb84eafe2f7"}