{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:5IRDRMF5PE4KVRRK4SWRHQZPVE","short_pith_number":"pith:5IRDRMF5","schema_version":"1.0","canonical_sha256":"ea2238b0bd7938aac62ae4ad13c32fa92c2803a7e39427bd2ba8ec5d67836b47","source":{"kind":"arxiv","id":"1203.2651","version":1},"attestation_state":"computed","paper":{"title":"Chow groups of smooth varieties fibred by quadrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Charles Vial","submitted_at":"2012-03-12T21:03:41Z","abstract_excerpt":"Let $f : X \\rightarrow B$ be a proper flat dominant morphism between two smooth quasi-projective complex varieties $X$ and $B$. Assume that there exists an integer $l$ such that all closed fibres $X_b$ of $f$ satisfy $CH_j(X_b) = \\Q$ for all $j \\leq l$. Then we prove an analogue of the projective bundle formula for $CH_i(X)$ for $i \\leq l$. When $B$ is a surface, $X$ is projective and $l = \\lfloor \\frac{\\dim X - 3}{2} \\rfloor$, this makes it possible to construct a Chow-K\\\"unneth decomposition for $X$ that satisfies Murre's conjectures. For instance we prove Murre's conjectures for complex smo"},"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":"1203.2651","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-03-12T21:03:41Z","cross_cats_sorted":[],"title_canon_sha256":"56d6ca405d2716da2a4c5abf6ee31c4d98e352c5fc8b28b8f4832f51d4f5b218","abstract_canon_sha256":"d0942b1af3533503f94605c864cee8cef973b9baa3a8a0a398468a21bbc6ea9d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:00:15.078250Z","signature_b64":"/T8nPPnL8+rD+u4zTijd5XmeEQZ8Htv7npbf88R1Dw182mDM+qX8hr3PgP+L/U8Ei2aHoUbh6K4hVbcokeJiCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea2238b0bd7938aac62ae4ad13c32fa92c2803a7e39427bd2ba8ec5d67836b47","last_reissued_at":"2026-05-18T04:00:15.077461Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:00:15.077461Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Chow groups of smooth varieties fibred by quadrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Charles Vial","submitted_at":"2012-03-12T21:03:41Z","abstract_excerpt":"Let $f : X \\rightarrow B$ be a proper flat dominant morphism between two smooth quasi-projective complex varieties $X$ and $B$. Assume that there exists an integer $l$ such that all closed fibres $X_b$ of $f$ satisfy $CH_j(X_b) = \\Q$ for all $j \\leq l$. Then we prove an analogue of the projective bundle formula for $CH_i(X)$ for $i \\leq l$. When $B$ is a surface, $X$ is projective and $l = \\lfloor \\frac{\\dim X - 3}{2} \\rfloor$, this makes it possible to construct a Chow-K\\\"unneth decomposition for $X$ that satisfies Murre's conjectures. For instance we prove Murre's conjectures for complex smo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2651","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":"1203.2651","created_at":"2026-05-18T04:00:15.077590+00:00"},{"alias_kind":"arxiv_version","alias_value":"1203.2651v1","created_at":"2026-05-18T04:00:15.077590+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2651","created_at":"2026-05-18T04:00:15.077590+00:00"},{"alias_kind":"pith_short_12","alias_value":"5IRDRMF5PE4K","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_16","alias_value":"5IRDRMF5PE4KVRRK","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_8","alias_value":"5IRDRMF5","created_at":"2026-05-18T12:26:53.410803+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/5IRDRMF5PE4KVRRK4SWRHQZPVE","json":"https://pith.science/pith/5IRDRMF5PE4KVRRK4SWRHQZPVE.json","graph_json":"https://pith.science/api/pith-number/5IRDRMF5PE4KVRRK4SWRHQZPVE/graph.json","events_json":"https://pith.science/api/pith-number/5IRDRMF5PE4KVRRK4SWRHQZPVE/events.json","paper":"https://pith.science/paper/5IRDRMF5"},"agent_actions":{"view_html":"https://pith.science/pith/5IRDRMF5PE4KVRRK4SWRHQZPVE","download_json":"https://pith.science/pith/5IRDRMF5PE4KVRRK4SWRHQZPVE.json","view_paper":"https://pith.science/paper/5IRDRMF5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1203.2651&json=true","fetch_graph":"https://pith.science/api/pith-number/5IRDRMF5PE4KVRRK4SWRHQZPVE/graph.json","fetch_events":"https://pith.science/api/pith-number/5IRDRMF5PE4KVRRK4SWRHQZPVE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5IRDRMF5PE4KVRRK4SWRHQZPVE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5IRDRMF5PE4KVRRK4SWRHQZPVE/action/storage_attestation","attest_author":"https://pith.science/pith/5IRDRMF5PE4KVRRK4SWRHQZPVE/action/author_attestation","sign_citation":"https://pith.science/pith/5IRDRMF5PE4KVRRK4SWRHQZPVE/action/citation_signature","submit_replication":"https://pith.science/pith/5IRDRMF5PE4KVRRK4SWRHQZPVE/action/replication_record"}},"created_at":"2026-05-18T04:00:15.077590+00:00","updated_at":"2026-05-18T04:00:15.077590+00:00"}