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We show using Kahn's and Sujatha's theory of birational motives that a Chow motive over $k$ whose Chow groups are all representable belongs to the full and thick subcategory of motives generated by the twisted motives of curves.\n  --\n  Motifs purs dont les groupes de Chow sont repr\\'esentables.\n  Soit $k$ un corps alg\\'ebriquement clos. Nous prouvons, en nous servant de la th\\'eorie des motifs birationnels d\\'evelopp\\'ee par Kahn et Sujatha, qu'un motif de Chow d\\'efini sur $k$ dont les groupes de Chow sont tous repr\\'esentables appartient \\`a la sous-"},"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":"1111.3662","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-11-15T21:35:33Z","cross_cats_sorted":[],"title_canon_sha256":"2754b2c66923ac04026a1f5abb5f9b05501917db1c42b9b59e98eaafe5ad2dc7","abstract_canon_sha256":"685ea86f4d65570cd5e69413a74357b79553480d1cd27410e1007df11f9a13d7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:13.759128Z","signature_b64":"gFwXRtQd90CXopmjvjLV3AvKE80VPVPF6j0xoq0462VkmvdcxGou2zCUwJr9mk/JWD3vjoj0VUYkgP2HehzYDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e0b43a3f7889aab7725f2bb56be16dd8c76ae25373e2e218d98a727668568cc","last_reissued_at":"2026-05-18T04:08:13.758722Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:13.758722Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pure motives with representable Chow groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Charles Vial","submitted_at":"2011-11-15T21:35:33Z","abstract_excerpt":"Let $k$ be an algebraically closed field. We show using Kahn's and Sujatha's theory of birational motives that a Chow motive over $k$ whose Chow groups are all representable belongs to the full and thick subcategory of motives generated by the twisted motives of curves.\n  --\n  Motifs purs dont les groupes de Chow sont repr\\'esentables.\n  Soit $k$ un corps alg\\'ebriquement clos. Nous prouvons, en nous servant de la th\\'eorie des motifs birationnels d\\'evelopp\\'ee par Kahn et Sujatha, qu'un motif de Chow d\\'efini sur $k$ dont les groupes de Chow sont tous repr\\'esentables appartient \\`a la sous-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3662","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":"1111.3662","created_at":"2026-05-18T04:08:13.758782+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.3662v1","created_at":"2026-05-18T04:08:13.758782+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.3662","created_at":"2026-05-18T04:08:13.758782+00:00"},{"alias_kind":"pith_short_12","alias_value":"FYFUHI7XRCNK","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_16","alias_value":"FYFUHI7XRCNKW5ZF","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_8","alias_value":"FYFUHI7X","created_at":"2026-05-18T12:26:28.662955+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/FYFUHI7XRCNKW5ZF6K5VNPQW3W","json":"https://pith.science/pith/FYFUHI7XRCNKW5ZF6K5VNPQW3W.json","graph_json":"https://pith.science/api/pith-number/FYFUHI7XRCNKW5ZF6K5VNPQW3W/graph.json","events_json":"https://pith.science/api/pith-number/FYFUHI7XRCNKW5ZF6K5VNPQW3W/events.json","paper":"https://pith.science/paper/FYFUHI7X"},"agent_actions":{"view_html":"https://pith.science/pith/FYFUHI7XRCNKW5ZF6K5VNPQW3W","download_json":"https://pith.science/pith/FYFUHI7XRCNKW5ZF6K5VNPQW3W.json","view_paper":"https://pith.science/paper/FYFUHI7X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.3662&json=true","fetch_graph":"https://pith.science/api/pith-number/FYFUHI7XRCNKW5ZF6K5VNPQW3W/graph.json","fetch_events":"https://pith.science/api/pith-number/FYFUHI7XRCNKW5ZF6K5VNPQW3W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FYFUHI7XRCNKW5ZF6K5VNPQW3W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FYFUHI7XRCNKW5ZF6K5VNPQW3W/action/storage_attestation","attest_author":"https://pith.science/pith/FYFUHI7XRCNKW5ZF6K5VNPQW3W/action/author_attestation","sign_citation":"https://pith.science/pith/FYFUHI7XRCNKW5ZF6K5VNPQW3W/action/citation_signature","submit_replication":"https://pith.science/pith/FYFUHI7XRCNKW5ZF6K5VNPQW3W/action/replication_record"}},"created_at":"2026-05-18T04:08:13.758782+00:00","updated_at":"2026-05-18T04:08:13.758782+00:00"}