{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:L3H2VFHB6D3TZ6RKOGPYDOZQIR","short_pith_number":"pith:L3H2VFHB","schema_version":"1.0","canonical_sha256":"5ecfaa94e1f0f73cfa2a719f81bb304445b3717a5fceb48df58b1f1c963626a3","source":{"kind":"arxiv","id":"1012.5367","version":2},"attestation_state":"computed","paper":{"title":"Degree three cohomology of function fields of surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"R. Parimala, V. Suresh","submitted_at":"2010-12-24T09:12:17Z","abstract_excerpt":"Let F be a finite field and l a prime not equal to the characteristic of F. Let K be the function field of a surface over F. Assume that K contains a primitive lth root of unity. In the paper we prove a certain local-global principle for elements of H^3(K, {\\mu}_l) in terms of symbols in H^2(K, {\\mu}_l) with respect to discrete valuations of K. We also show that this local global principle is equivalent to the vanishing of certain unramified cohomology groups of 3-folds over finite fields. Using this local-global principle we show that every element in H^3(F, {\\mu}_l) is a symbol. The vanishin"},"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":"1012.5367","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-12-24T09:12:17Z","cross_cats_sorted":[],"title_canon_sha256":"a7baf61cb348b2003d7a8d8293940bc373b21928341d43a42c89a52fd9f90d4b","abstract_canon_sha256":"c2fb571557b3b30a89d27ed9274452294651a8950d5824eca561ad64d10a3f78"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:24.622252Z","signature_b64":"PvpIwsgnWqQB/RtMU4Pu5WxI6ty97eHJqj1agOPpvFjjO6epUvdRWlbC+QSu52ycsJA4/k7H+2oOHKs3NuQvDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ecfaa94e1f0f73cfa2a719f81bb304445b3717a5fceb48df58b1f1c963626a3","last_reissued_at":"2026-05-18T02:50:24.621740Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:24.621740Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Degree three cohomology of function fields of surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"R. Parimala, V. Suresh","submitted_at":"2010-12-24T09:12:17Z","abstract_excerpt":"Let F be a finite field and l a prime not equal to the characteristic of F. Let K be the function field of a surface over F. Assume that K contains a primitive lth root of unity. In the paper we prove a certain local-global principle for elements of H^3(K, {\\mu}_l) in terms of symbols in H^2(K, {\\mu}_l) with respect to discrete valuations of K. We also show that this local global principle is equivalent to the vanishing of certain unramified cohomology groups of 3-folds over finite fields. Using this local-global principle we show that every element in H^3(F, {\\mu}_l) is a symbol. The vanishin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5367","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":"1012.5367","created_at":"2026-05-18T02:50:24.621819+00:00"},{"alias_kind":"arxiv_version","alias_value":"1012.5367v2","created_at":"2026-05-18T02:50:24.621819+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5367","created_at":"2026-05-18T02:50:24.621819+00:00"},{"alias_kind":"pith_short_12","alias_value":"L3H2VFHB6D3T","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"L3H2VFHB6D3TZ6RK","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"L3H2VFHB","created_at":"2026-05-18T12:26:09.077623+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/L3H2VFHB6D3TZ6RKOGPYDOZQIR","json":"https://pith.science/pith/L3H2VFHB6D3TZ6RKOGPYDOZQIR.json","graph_json":"https://pith.science/api/pith-number/L3H2VFHB6D3TZ6RKOGPYDOZQIR/graph.json","events_json":"https://pith.science/api/pith-number/L3H2VFHB6D3TZ6RKOGPYDOZQIR/events.json","paper":"https://pith.science/paper/L3H2VFHB"},"agent_actions":{"view_html":"https://pith.science/pith/L3H2VFHB6D3TZ6RKOGPYDOZQIR","download_json":"https://pith.science/pith/L3H2VFHB6D3TZ6RKOGPYDOZQIR.json","view_paper":"https://pith.science/paper/L3H2VFHB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1012.5367&json=true","fetch_graph":"https://pith.science/api/pith-number/L3H2VFHB6D3TZ6RKOGPYDOZQIR/graph.json","fetch_events":"https://pith.science/api/pith-number/L3H2VFHB6D3TZ6RKOGPYDOZQIR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L3H2VFHB6D3TZ6RKOGPYDOZQIR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L3H2VFHB6D3TZ6RKOGPYDOZQIR/action/storage_attestation","attest_author":"https://pith.science/pith/L3H2VFHB6D3TZ6RKOGPYDOZQIR/action/author_attestation","sign_citation":"https://pith.science/pith/L3H2VFHB6D3TZ6RKOGPYDOZQIR/action/citation_signature","submit_replication":"https://pith.science/pith/L3H2VFHB6D3TZ6RKOGPYDOZQIR/action/replication_record"}},"created_at":"2026-05-18T02:50:24.621819+00:00","updated_at":"2026-05-18T02:50:24.621819+00:00"}