{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:2IOVELP2TZPR2ERI43TDDKTYSJ","short_pith_number":"pith:2IOVELP2","schema_version":"1.0","canonical_sha256":"d21d522dfa9e5f1d1228e6e631aa78925b9d93ed7d8c786338f9df1d81463dc5","source":{"kind":"arxiv","id":"1207.1896","version":2},"attestation_state":"computed","paper":{"title":"Local cohomology modules of polynomial or power series rings over rings of small dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Luis Nunez-Betancourt","submitted_at":"2012-07-08T18:08:34Z","abstract_excerpt":"Let $A$ be a ring and $R$ be a polynomial or a power series ring over $A$. When $A$ has dimension zero, we show that the Bass numbers and the associated primes of the local cohomology modules over $R$ are finite. Moreover, if $A$ has dimension one and $\\pi$ is an nonzero divisor, then the same properties hold for prime ideals that contain $\\pi.$ These results do not require that $A$ contains a field. As a consequence, we give a different proof for the finiteness properties of local cohomology over unramified regular local rings. In addition, we extend previous results on the injective dimensio"},"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":"1207.1896","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-07-08T18:08:34Z","cross_cats_sorted":[],"title_canon_sha256":"27ccacb4f539c5ba64f15ed60e354147150ecae5646bb6b83e2b84c73ba44137","abstract_canon_sha256":"908ad4f5413b5c2918b0f28ad183aab633e166cd01ccdbba641035ff9223d2e8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:08:25.167270Z","signature_b64":"KuaI55j04HaeE6ksotorH9l1ORVHRse6sMXat/3BudmcmmhEqbMSvqTqQ1iEye6q0JPo+j2G73WAi3eVp1o9BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d21d522dfa9e5f1d1228e6e631aa78925b9d93ed7d8c786338f9df1d81463dc5","last_reissued_at":"2026-05-18T03:08:25.166672Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:08:25.166672Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local cohomology modules of polynomial or power series rings over rings of small dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Luis Nunez-Betancourt","submitted_at":"2012-07-08T18:08:34Z","abstract_excerpt":"Let $A$ be a ring and $R$ be a polynomial or a power series ring over $A$. When $A$ has dimension zero, we show that the Bass numbers and the associated primes of the local cohomology modules over $R$ are finite. Moreover, if $A$ has dimension one and $\\pi$ is an nonzero divisor, then the same properties hold for prime ideals that contain $\\pi.$ These results do not require that $A$ contains a field. As a consequence, we give a different proof for the finiteness properties of local cohomology over unramified regular local rings. In addition, we extend previous results on the injective dimensio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1896","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1207.1896","created_at":"2026-05-18T03:08:25.166766+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.1896v2","created_at":"2026-05-18T03:08:25.166766+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.1896","created_at":"2026-05-18T03:08:25.166766+00:00"},{"alias_kind":"pith_short_12","alias_value":"2IOVELP2TZPR","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_16","alias_value":"2IOVELP2TZPR2ERI","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_8","alias_value":"2IOVELP2","created_at":"2026-05-18T12:26:50.516681+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2IOVELP2TZPR2ERI43TDDKTYSJ","json":"https://pith.science/pith/2IOVELP2TZPR2ERI43TDDKTYSJ.json","graph_json":"https://pith.science/api/pith-number/2IOVELP2TZPR2ERI43TDDKTYSJ/graph.json","events_json":"https://pith.science/api/pith-number/2IOVELP2TZPR2ERI43TDDKTYSJ/events.json","paper":"https://pith.science/paper/2IOVELP2"},"agent_actions":{"view_html":"https://pith.science/pith/2IOVELP2TZPR2ERI43TDDKTYSJ","download_json":"https://pith.science/pith/2IOVELP2TZPR2ERI43TDDKTYSJ.json","view_paper":"https://pith.science/paper/2IOVELP2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.1896&json=true","fetch_graph":"https://pith.science/api/pith-number/2IOVELP2TZPR2ERI43TDDKTYSJ/graph.json","fetch_events":"https://pith.science/api/pith-number/2IOVELP2TZPR2ERI43TDDKTYSJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2IOVELP2TZPR2ERI43TDDKTYSJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2IOVELP2TZPR2ERI43TDDKTYSJ/action/storage_attestation","attest_author":"https://pith.science/pith/2IOVELP2TZPR2ERI43TDDKTYSJ/action/author_attestation","sign_citation":"https://pith.science/pith/2IOVELP2TZPR2ERI43TDDKTYSJ/action/citation_signature","submit_replication":"https://pith.science/pith/2IOVELP2TZPR2ERI43TDDKTYSJ/action/replication_record"}},"created_at":"2026-05-18T03:08:25.166766+00:00","updated_at":"2026-05-18T03:08:25.166766+00:00"}