{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:WPZHDKAXIV3KR5VFEZYSAVDTI4","short_pith_number":"pith:WPZHDKAX","schema_version":"1.0","canonical_sha256":"b3f271a8174576a8f6a5267120547347297a8c2c39e13d04de05a8d849ef262a","source":{"kind":"arxiv","id":"1211.5748","version":2},"attestation_state":"computed","paper":{"title":"Cofiniteness of weakly Laskerian local cohomology modules","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Kamal Bahmanpour, Moharram Aghapournahr","submitted_at":"2012-11-25T09:37:09Z","abstract_excerpt":"Let $I$ be an ideal of a Noetherian ring R and M be a finitely generated R-module. We introduce the class of extension modules of finitely generated modules by the class of all modules $T$ with $\\dim T\\leq n$ and we show it by ${\\rm FD_{\\leq n}}$ where $n\\geq -1$ is an integer. We prove that for any ${\\rm FD_{\\leq 0}}$(or minimax) submodule N of $H^t_I(M)$ the R-modules ${\\rm Hom}_R(R/I,H^{t}_I(M)/N)   {\\rm and}   {\\rm Ext}^1_R(R/I,H^{t}_I(M)/N)$ are finitely generated, whenever the modules $H^0_I(M)$, $H^1_I(M)$, ..., $H^{t-1}_I(M)$ are ${\\rm FD_{\\leq 1}}$ (or weakly Laskerian). As a conseque"},"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":"1211.5748","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.AC","submitted_at":"2012-11-25T09:37:09Z","cross_cats_sorted":[],"title_canon_sha256":"2b6401bf81248fd076bfa45f74be0be89a8bf419613ef471bd05e7d28e8f8d37","abstract_canon_sha256":"5990e11fcd4a99a7ed571fc2236adc629b8e5764c226d55fae3d5a38181e6c28"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:05.430402Z","signature_b64":"JkS++k1oUJk3pn8wI0Cxq4fLnMjStIloTuylnYuaTdqQuIYHAzVMf/PaGp/UEEyAdqNPARvMzE+T+2OhMBk9AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3f271a8174576a8f6a5267120547347297a8c2c39e13d04de05a8d849ef262a","last_reissued_at":"2026-05-18T02:25:05.429968Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:05.429968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cofiniteness of weakly Laskerian local cohomology modules","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Kamal Bahmanpour, Moharram Aghapournahr","submitted_at":"2012-11-25T09:37:09Z","abstract_excerpt":"Let $I$ be an ideal of a Noetherian ring R and M be a finitely generated R-module. We introduce the class of extension modules of finitely generated modules by the class of all modules $T$ with $\\dim T\\leq n$ and we show it by ${\\rm FD_{\\leq n}}$ where $n\\geq -1$ is an integer. We prove that for any ${\\rm FD_{\\leq 0}}$(or minimax) submodule N of $H^t_I(M)$ the R-modules ${\\rm Hom}_R(R/I,H^{t}_I(M)/N)   {\\rm and}   {\\rm Ext}^1_R(R/I,H^{t}_I(M)/N)$ are finitely generated, whenever the modules $H^0_I(M)$, $H^1_I(M)$, ..., $H^{t-1}_I(M)$ are ${\\rm FD_{\\leq 1}}$ (or weakly Laskerian). 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