{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:6VEMRTEUWHKOLFHN5ENFZAYBOQ","short_pith_number":"pith:6VEMRTEU","schema_version":"1.0","canonical_sha256":"f548c8cc94b1d4e594ede91a5c83017404c971e727105137595a766c0fb433c0","source":{"kind":"arxiv","id":"1810.12628","version":2},"attestation_state":"computed","paper":{"title":"Smoothness of stabilisers in generic characteristic","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AC","math.AG","math.RT"],"primary_cat":"math.GR","authors_text":"Benjamin Martin, David I. Stewart, Lewis Topley","submitted_at":"2018-10-30T10:21:24Z","abstract_excerpt":"Let $R$ be a commutative unital ring. Given a finitely presented affine $R$-group scheme $G$ acting on a separated scheme $X$ of finite type over $R$, we show that there is a prime $p_0$ such that for any $R$-algebra $k$ which is an algebraically closed field of characteristic $p\\geq p_0$, the centraliser in $G_k$ of any closed subscheme of $X_k$ is smooth. When $X$ is not necessarily separated we show similarly that for any closed subscheme $Y \\subseteq X$ there is a $p_1$ depending on $Y$ such that when $k$ has characteristic $p \\geq p_1$ the normaliser of $Y$ in $G_k$ is smooth. We prove th"},"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":"1810.12628","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2018-10-30T10:21:24Z","cross_cats_sorted":["math.AC","math.AG","math.RT"],"title_canon_sha256":"280b8164b69bf12ea6252781580d24f10e55c50e4219cb5db2ab5c9f5336df08","abstract_canon_sha256":"e6102c887150f27f0483e8c54243741a9123a1ea5730a88e2bfe709960842dbc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-27T14:06:32.192401Z","signature_b64":"oDiNDOpIlpsFY/opgd9Kbx0wf8yVj85i0QpUBfcRzXshQ+4SR4CAqf9z3Fli9SuS+sN+trEynsUhbFAMGf/aCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f548c8cc94b1d4e594ede91a5c83017404c971e727105137595a766c0fb433c0","last_reissued_at":"2026-05-27T14:06:32.189738Z","signature_status":"signed_v1","first_computed_at":"2026-05-27T14:06:32.189738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Smoothness of stabilisers in generic characteristic","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AC","math.AG","math.RT"],"primary_cat":"math.GR","authors_text":"Benjamin Martin, David I. Stewart, Lewis Topley","submitted_at":"2018-10-30T10:21:24Z","abstract_excerpt":"Let $R$ be a commutative unital ring. Given a finitely presented affine $R$-group scheme $G$ acting on a separated scheme $X$ of finite type over $R$, we show that there is a prime $p_0$ such that for any $R$-algebra $k$ which is an algebraically closed field of characteristic $p\\geq p_0$, the centraliser in $G_k$ of any closed subscheme of $X_k$ is smooth. When $X$ is not necessarily separated we show similarly that for any closed subscheme $Y \\subseteq X$ there is a $p_1$ depending on $Y$ such that when $k$ has characteristic $p \\geq p_1$ the normaliser of $Y$ in $G_k$ is smooth. We prove th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12628","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1810.12628/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1810.12628","created_at":"2026-05-27T14:06:32.189844+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.12628v2","created_at":"2026-05-27T14:06:32.189844+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.12628","created_at":"2026-05-27T14:06:32.189844+00:00"},{"alias_kind":"pith_short_12","alias_value":"6VEMRTEUWHKO","created_at":"2026-05-27T14:06:32.189844+00:00"},{"alias_kind":"pith_short_16","alias_value":"6VEMRTEUWHKOLFHN","created_at":"2026-05-27T14:06:32.189844+00:00"},{"alias_kind":"pith_short_8","alias_value":"6VEMRTEU","created_at":"2026-05-27T14:06:32.189844+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/6VEMRTEUWHKOLFHN5ENFZAYBOQ","json":"https://pith.science/pith/6VEMRTEUWHKOLFHN5ENFZAYBOQ.json","graph_json":"https://pith.science/api/pith-number/6VEMRTEUWHKOLFHN5ENFZAYBOQ/graph.json","events_json":"https://pith.science/api/pith-number/6VEMRTEUWHKOLFHN5ENFZAYBOQ/events.json","paper":"https://pith.science/paper/6VEMRTEU"},"agent_actions":{"view_html":"https://pith.science/pith/6VEMRTEUWHKOLFHN5ENFZAYBOQ","download_json":"https://pith.science/pith/6VEMRTEUWHKOLFHN5ENFZAYBOQ.json","view_paper":"https://pith.science/paper/6VEMRTEU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.12628&json=true","fetch_graph":"https://pith.science/api/pith-number/6VEMRTEUWHKOLFHN5ENFZAYBOQ/graph.json","fetch_events":"https://pith.science/api/pith-number/6VEMRTEUWHKOLFHN5ENFZAYBOQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6VEMRTEUWHKOLFHN5ENFZAYBOQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6VEMRTEUWHKOLFHN5ENFZAYBOQ/action/storage_attestation","attest_author":"https://pith.science/pith/6VEMRTEUWHKOLFHN5ENFZAYBOQ/action/author_attestation","sign_citation":"https://pith.science/pith/6VEMRTEUWHKOLFHN5ENFZAYBOQ/action/citation_signature","submit_replication":"https://pith.science/pith/6VEMRTEUWHKOLFHN5ENFZAYBOQ/action/replication_record"}},"created_at":"2026-05-27T14:06:32.189844+00:00","updated_at":"2026-05-27T14:06:32.189844+00:00"}