{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:A4J7IKUYMBP7FDNH34SPRFCEIZ","short_pith_number":"pith:A4J7IKUY","schema_version":"1.0","canonical_sha256":"0713f42a98605ff28da7df24f8944446486b94977f1874b3b345d70f40ad8018","source":{"kind":"arxiv","id":"1101.3938","version":3},"attestation_state":"computed","paper":{"title":"On embeddings of certain spherical homogeneous spaces in prime characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.AG","authors_text":"Rudolf Tange","submitted_at":"2011-01-20T15:59:01Z","abstract_excerpt":"Let $\\mc G$ be a reductive group over an algebraically closed field of characteristic $p>0$. We study homogeneous $\\mc G$-spaces that are induced from the $G\\times G$-space $G$, $G$ a suitable reductive group, along a parabolic subgroup of $\\mc G$. We show that, under certain mild assumptions, any (normal) equivariant embedding of such a homogeneous space is canonically Frobenius split compatible with certain subvarieties and has an equivariant rational resolution by a toroidal embedding. In particular, all these embeddings are Cohen-Macaulay.\n  Examples are the $G\\times G$-orbits in normal re"},"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":"1101.3938","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-01-20T15:59:01Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"55cacd4e319eee9144b22eef0278dba690c82e40c63cf9ffb4c58255dceabba9","abstract_canon_sha256":"c001dd5e6c7ae25a47a3109ab96adbc49f38782594764e1a4364ec0ff1f9b9ba"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:51:36.020780Z","signature_b64":"HrBKh6yghaS0ujtzp2/1MfvoJ/uOr51BxJNN5NYG8gUTArEEvVMDLsrzg9UflhxgeKhri2MgYW0CyB8Op52LBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0713f42a98605ff28da7df24f8944446486b94977f1874b3b345d70f40ad8018","last_reissued_at":"2026-05-18T03:51:36.019921Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:51:36.019921Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On embeddings of certain spherical homogeneous spaces in prime characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.AG","authors_text":"Rudolf Tange","submitted_at":"2011-01-20T15:59:01Z","abstract_excerpt":"Let $\\mc G$ be a reductive group over an algebraically closed field of characteristic $p>0$. We study homogeneous $\\mc G$-spaces that are induced from the $G\\times G$-space $G$, $G$ a suitable reductive group, along a parabolic subgroup of $\\mc G$. We show that, under certain mild assumptions, any (normal) equivariant embedding of such a homogeneous space is canonically Frobenius split compatible with certain subvarieties and has an equivariant rational resolution by a toroidal embedding. In particular, all these embeddings are Cohen-Macaulay.\n  Examples are the $G\\times G$-orbits in normal re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3938","kind":"arxiv","version":3},"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":"1101.3938","created_at":"2026-05-18T03:51:36.020059+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.3938v3","created_at":"2026-05-18T03:51:36.020059+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.3938","created_at":"2026-05-18T03:51:36.020059+00:00"},{"alias_kind":"pith_short_12","alias_value":"A4J7IKUYMBP7","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_16","alias_value":"A4J7IKUYMBP7FDNH","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_8","alias_value":"A4J7IKUY","created_at":"2026-05-18T12:26:24.575870+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/A4J7IKUYMBP7FDNH34SPRFCEIZ","json":"https://pith.science/pith/A4J7IKUYMBP7FDNH34SPRFCEIZ.json","graph_json":"https://pith.science/api/pith-number/A4J7IKUYMBP7FDNH34SPRFCEIZ/graph.json","events_json":"https://pith.science/api/pith-number/A4J7IKUYMBP7FDNH34SPRFCEIZ/events.json","paper":"https://pith.science/paper/A4J7IKUY"},"agent_actions":{"view_html":"https://pith.science/pith/A4J7IKUYMBP7FDNH34SPRFCEIZ","download_json":"https://pith.science/pith/A4J7IKUYMBP7FDNH34SPRFCEIZ.json","view_paper":"https://pith.science/paper/A4J7IKUY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.3938&json=true","fetch_graph":"https://pith.science/api/pith-number/A4J7IKUYMBP7FDNH34SPRFCEIZ/graph.json","fetch_events":"https://pith.science/api/pith-number/A4J7IKUYMBP7FDNH34SPRFCEIZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A4J7IKUYMBP7FDNH34SPRFCEIZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A4J7IKUYMBP7FDNH34SPRFCEIZ/action/storage_attestation","attest_author":"https://pith.science/pith/A4J7IKUYMBP7FDNH34SPRFCEIZ/action/author_attestation","sign_citation":"https://pith.science/pith/A4J7IKUYMBP7FDNH34SPRFCEIZ/action/citation_signature","submit_replication":"https://pith.science/pith/A4J7IKUYMBP7FDNH34SPRFCEIZ/action/replication_record"}},"created_at":"2026-05-18T03:51:36.020059+00:00","updated_at":"2026-05-18T03:51:36.020059+00:00"}