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When H is of maximal rank in G, we also prove that G/H is rational if the maximal semisimple quotient of G is isogenous to a product of almost-simple groups of type A, type C (when characteristic(k) is not 2), or type B_3 or G_2 (when characteristic(k) = 0)."},"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":"1504.05402","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-04-21T12:26:22Z","cross_cats_sorted":[],"title_canon_sha256":"b1fe363d1c0fef54a36860efa729b818ec6af821769210e33a2a5c1f6a0bae60","abstract_canon_sha256":"028dfd3323ceae1f0c6af604e3ddfe3a57b4b0de2e35e12bce8dc39eae8199c4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:14.908646Z","signature_b64":"csKQCV81Oxk0UadTj/ilEYMw6yf7x49QhpaGrjcJv3H3URsxTTB7JrUPdi4zFQwvrdt3tJCmc0rjqFuJYdhtAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ebfce261775cf9fa4c6976df77d15c43b249cebf164c5057b8a63b434544dd4","last_reissued_at":"2026-05-18T00:05:14.907925Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:14.907925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rationality of homogeneous varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"CheeWhye Chin, De-Qi Zhang","submitted_at":"2015-04-21T12:26:22Z","abstract_excerpt":"Let G be a connected linear algebraic group over an algebraically closed field k, and let H be a connected closed subgroup of G. We prove that the homogeneous variety G/H is a rational variety over k whenever H is solvable, or when dim(G/H) < 11 and characteristic(k) = 0. When H is of maximal rank in G, we also prove that G/H is rational if the maximal semisimple quotient of G is isogenous to a product of almost-simple groups of type A, type C (when characteristic(k) is not 2), or type B_3 or G_2 (when characteristic(k) = 0)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05402","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":"1504.05402","created_at":"2026-05-18T00:05:14.908049+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.05402v2","created_at":"2026-05-18T00:05:14.908049+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05402","created_at":"2026-05-18T00:05:14.908049+00:00"},{"alias_kind":"pith_short_12","alias_value":"H2744JQXOXHZ","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"H2744JQXOXHZ7JGG","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"H2744JQX","created_at":"2026-05-18T12:29:22.688609+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/H2744JQXOXHZ7JGGS5W7O7IVYQ","json":"https://pith.science/pith/H2744JQXOXHZ7JGGS5W7O7IVYQ.json","graph_json":"https://pith.science/api/pith-number/H2744JQXOXHZ7JGGS5W7O7IVYQ/graph.json","events_json":"https://pith.science/api/pith-number/H2744JQXOXHZ7JGGS5W7O7IVYQ/events.json","paper":"https://pith.science/paper/H2744JQX"},"agent_actions":{"view_html":"https://pith.science/pith/H2744JQXOXHZ7JGGS5W7O7IVYQ","download_json":"https://pith.science/pith/H2744JQXOXHZ7JGGS5W7O7IVYQ.json","view_paper":"https://pith.science/paper/H2744JQX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.05402&json=true","fetch_graph":"https://pith.science/api/pith-number/H2744JQXOXHZ7JGGS5W7O7IVYQ/graph.json","fetch_events":"https://pith.science/api/pith-number/H2744JQXOXHZ7JGGS5W7O7IVYQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H2744JQXOXHZ7JGGS5W7O7IVYQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H2744JQXOXHZ7JGGS5W7O7IVYQ/action/storage_attestation","attest_author":"https://pith.science/pith/H2744JQXOXHZ7JGGS5W7O7IVYQ/action/author_attestation","sign_citation":"https://pith.science/pith/H2744JQXOXHZ7JGGS5W7O7IVYQ/action/citation_signature","submit_replication":"https://pith.science/pith/H2744JQXOXHZ7JGGS5W7O7IVYQ/action/replication_record"}},"created_at":"2026-05-18T00:05:14.908049+00:00","updated_at":"2026-05-18T00:05:14.908049+00:00"}