{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:A4J7IKUYMBP7FDNH34SPRFCEIZ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"c001dd5e6c7ae25a47a3109ab96adbc49f38782594764e1a4364ec0ff1f9b9ba","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-01-20T15:59:01Z","title_canon_sha256":"55cacd4e319eee9144b22eef0278dba690c82e40c63cf9ffb4c58255dceabba9"},"schema_version":"1.0","source":{"id":"1101.3938","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.3938","created_at":"2026-05-18T03:51:36Z"},{"alias_kind":"arxiv_version","alias_value":"1101.3938v3","created_at":"2026-05-18T03:51:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.3938","created_at":"2026-05-18T03:51:36Z"},{"alias_kind":"pith_short_12","alias_value":"A4J7IKUYMBP7","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"A4J7IKUYMBP7FDNH","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"A4J7IKUY","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:a5c63e633d1925a466c4e206741f0f9363433d1193f584e3c825be5172fe02a5","target":"graph","created_at":"2026-05-18T03:51:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Rudolf Tange","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-01-20T15:59:01Z","title":"On embeddings of certain spherical homogeneous spaces in prime characteristic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3938","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:424bddb9ca9cc899f410bab0d0e4f64c9265eccd41e9937b19b35f07dea40670","target":"record","created_at":"2026-05-18T03:51:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c001dd5e6c7ae25a47a3109ab96adbc49f38782594764e1a4364ec0ff1f9b9ba","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-01-20T15:59:01Z","title_canon_sha256":"55cacd4e319eee9144b22eef0278dba690c82e40c63cf9ffb4c58255dceabba9"},"schema_version":"1.0","source":{"id":"1101.3938","kind":"arxiv","version":3}},"canonical_sha256":"0713f42a98605ff28da7df24f8944446486b94977f1874b3b345d70f40ad8018","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0713f42a98605ff28da7df24f8944446486b94977f1874b3b345d70f40ad8018","first_computed_at":"2026-05-18T03:51:36.019921Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:36.019921Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HrBKh6yghaS0ujtzp2/1MfvoJ/uOr51BxJNN5NYG8gUTArEEvVMDLsrzg9UflhxgeKhri2MgYW0CyB8Op52LBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:36.020780Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.3938","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:424bddb9ca9cc899f410bab0d0e4f64c9265eccd41e9937b19b35f07dea40670","sha256:a5c63e633d1925a466c4e206741f0f9363433d1193f584e3c825be5172fe02a5"],"state_sha256":"1db785b5abf4aa980df219503ab0833c59c2883a79d9a03f5bbc1e58d34e9239"}