{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:7OJUKKBHJP635YRQT3QFUXT4D6","short_pith_number":"pith:7OJUKKBH","schema_version":"1.0","canonical_sha256":"fb934528274bfdbee2309ee05a5e7c1fbf8b63d1195897e7e71c8fdb55e2dc9d","source":{"kind":"arxiv","id":"1406.0247","version":1},"attestation_state":"computed","paper":{"title":"Proof of Grothendieck--Serre conjecture on principal G-bundles over regular local rings containing a finite field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ivan Panin","submitted_at":"2014-06-02T05:16:05Z","abstract_excerpt":"Let R be a regular local ring, containing a finite field. Let G be a reductive group scheme over R. We prove that a principal G-bundle over R is trivial, if it is trivial over the fraction field of R. In other words, if K is the fraction field of R, then the map of pointed sets H^1_{et}(R,G) \\to H^1_{et}(K,G), induced by the inclusion of R into K, has a trivial kernel. Certain arguments used in the present preprint do not work if the ring R contains a characteristic zero field. In that case and, more generally, in the case when the regular local ring R contains an infinite field this result is"},"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":"1406.0247","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-06-02T05:16:05Z","cross_cats_sorted":[],"title_canon_sha256":"0eb559d44796a0c7debf1d9546fc989960770764376202c8983dc4e7df37cd6f","abstract_canon_sha256":"888d7ab68c36b01b9005751a034ca5538250049adf6f049a82280dc50e2419b1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:41.377376Z","signature_b64":"SDL0bdyDbVJYPZ5RB5Zu6Dp2Ql/u59m7iCfJZC1w7CPVkNVB+k1wVGYOyM80rE5o227PLOdy0TEYiXz77Sd4Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb934528274bfdbee2309ee05a5e7c1fbf8b63d1195897e7e71c8fdb55e2dc9d","last_reissued_at":"2026-05-18T02:50:41.376675Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:41.376675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Proof of Grothendieck--Serre conjecture on principal G-bundles over regular local rings containing a finite field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ivan Panin","submitted_at":"2014-06-02T05:16:05Z","abstract_excerpt":"Let R be a regular local ring, containing a finite field. Let G be a reductive group scheme over R. We prove that a principal G-bundle over R is trivial, if it is trivial over the fraction field of R. In other words, if K is the fraction field of R, then the map of pointed sets H^1_{et}(R,G) \\to H^1_{et}(K,G), induced by the inclusion of R into K, has a trivial kernel. Certain arguments used in the present preprint do not work if the ring R contains a characteristic zero field. In that case and, more generally, in the case when the regular local ring R contains an infinite field this result is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.0247","kind":"arxiv","version":1},"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":"1406.0247","created_at":"2026-05-18T02:50:41.376772+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.0247v1","created_at":"2026-05-18T02:50:41.376772+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.0247","created_at":"2026-05-18T02:50:41.376772+00:00"},{"alias_kind":"pith_short_12","alias_value":"7OJUKKBHJP63","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_16","alias_value":"7OJUKKBHJP635YRQ","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_8","alias_value":"7OJUKKBH","created_at":"2026-05-18T12:28:19.803747+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/7OJUKKBHJP635YRQT3QFUXT4D6","json":"https://pith.science/pith/7OJUKKBHJP635YRQT3QFUXT4D6.json","graph_json":"https://pith.science/api/pith-number/7OJUKKBHJP635YRQT3QFUXT4D6/graph.json","events_json":"https://pith.science/api/pith-number/7OJUKKBHJP635YRQT3QFUXT4D6/events.json","paper":"https://pith.science/paper/7OJUKKBH"},"agent_actions":{"view_html":"https://pith.science/pith/7OJUKKBHJP635YRQT3QFUXT4D6","download_json":"https://pith.science/pith/7OJUKKBHJP635YRQT3QFUXT4D6.json","view_paper":"https://pith.science/paper/7OJUKKBH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.0247&json=true","fetch_graph":"https://pith.science/api/pith-number/7OJUKKBHJP635YRQT3QFUXT4D6/graph.json","fetch_events":"https://pith.science/api/pith-number/7OJUKKBHJP635YRQT3QFUXT4D6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7OJUKKBHJP635YRQT3QFUXT4D6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7OJUKKBHJP635YRQT3QFUXT4D6/action/storage_attestation","attest_author":"https://pith.science/pith/7OJUKKBHJP635YRQT3QFUXT4D6/action/author_attestation","sign_citation":"https://pith.science/pith/7OJUKKBHJP635YRQT3QFUXT4D6/action/citation_signature","submit_replication":"https://pith.science/pith/7OJUKKBHJP635YRQT3QFUXT4D6/action/replication_record"}},"created_at":"2026-05-18T02:50:41.376772+00:00","updated_at":"2026-05-18T02:50:41.376772+00:00"}