{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:IRMMZD6HYA6FSHHTDLGMOG2QYL","short_pith_number":"pith:IRMMZD6H","schema_version":"1.0","canonical_sha256":"4458cc8fc7c03c591cf31accc71b50c2d7963516a77fb910642ececa433568db","source":{"kind":"arxiv","id":"1809.04175","version":1},"attestation_state":"computed","paper":{"title":"On the geometry of the automorphism groups of affine varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.RT"],"primary_cat":"math.AG","authors_text":"Hanspeter Kraft, Jean-Philippe Furter","submitted_at":"2018-09-11T21:25:49Z","abstract_excerpt":"This article is a survey on ind-varieties and ind-groups introduced by Shafarevich in 1965, with a special emphasis on automorphism groups of affine varieties and actions of ind-groups on ind-varieties. We give precise definitions and complete proofs, including several known results. The survey contains many examples and also some questions which came up during our work on the subject.\n  Among the new results we show that for an affine variety X the automorphism group Aut(X) is always locally closed in the ind-semigroup End(X) of all endomorphisms, and we give an example of a strict closed sub"},"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":"1809.04175","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-09-11T21:25:49Z","cross_cats_sorted":["math.GR","math.RT"],"title_canon_sha256":"6ff7cf57190185382edcdf05fe6aef446cc437806637b9a864568e8ac1a10c40","abstract_canon_sha256":"2bcf4be3e64f39bac9cfb986b80e3a8e8164439d233bc58e5fca85b08233d3c7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:55.283001Z","signature_b64":"B1j6HpqYW/1R/R0Az7eC7CCJpsvsUzjFcWmTEbxsFnXd+CCzvU9dWHwZFAAdMzjXoz3pJNW7vnkMe4yVnlKiCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4458cc8fc7c03c591cf31accc71b50c2d7963516a77fb910642ececa433568db","last_reissued_at":"2026-05-18T00:05:55.282407Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:55.282407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the geometry of the automorphism groups of affine varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.RT"],"primary_cat":"math.AG","authors_text":"Hanspeter Kraft, Jean-Philippe Furter","submitted_at":"2018-09-11T21:25:49Z","abstract_excerpt":"This article is a survey on ind-varieties and ind-groups introduced by Shafarevich in 1965, with a special emphasis on automorphism groups of affine varieties and actions of ind-groups on ind-varieties. We give precise definitions and complete proofs, including several known results. The survey contains many examples and also some questions which came up during our work on the subject.\n  Among the new results we show that for an affine variety X the automorphism group Aut(X) is always locally closed in the ind-semigroup End(X) of all endomorphisms, and we give an example of a strict closed sub"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.04175","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":"1809.04175","created_at":"2026-05-18T00:05:55.282501+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.04175v1","created_at":"2026-05-18T00:05:55.282501+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.04175","created_at":"2026-05-18T00:05:55.282501+00:00"},{"alias_kind":"pith_short_12","alias_value":"IRMMZD6HYA6F","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_16","alias_value":"IRMMZD6HYA6FSHHT","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_8","alias_value":"IRMMZD6H","created_at":"2026-05-18T12:32:31.084164+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":4,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2605.20480","citing_title":"Infinite transitivity and polynomial vector fields","ref_index":12,"is_internal_anchor":true},{"citing_arxiv_id":"2510.17223","citing_title":"Borel subalgebras of Lie algebras of vector fields","ref_index":12,"is_internal_anchor":true},{"citing_arxiv_id":"2604.02864","citing_title":"Locally finite solvable Lie algebras of derivations","ref_index":7,"is_internal_anchor":false},{"citing_arxiv_id":"2604.04762","citing_title":"Isotropy subgroups of homogeneous locally nilpotent derivations","ref_index":14,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IRMMZD6HYA6FSHHTDLGMOG2QYL","json":"https://pith.science/pith/IRMMZD6HYA6FSHHTDLGMOG2QYL.json","graph_json":"https://pith.science/api/pith-number/IRMMZD6HYA6FSHHTDLGMOG2QYL/graph.json","events_json":"https://pith.science/api/pith-number/IRMMZD6HYA6FSHHTDLGMOG2QYL/events.json","paper":"https://pith.science/paper/IRMMZD6H"},"agent_actions":{"view_html":"https://pith.science/pith/IRMMZD6HYA6FSHHTDLGMOG2QYL","download_json":"https://pith.science/pith/IRMMZD6HYA6FSHHTDLGMOG2QYL.json","view_paper":"https://pith.science/paper/IRMMZD6H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.04175&json=true","fetch_graph":"https://pith.science/api/pith-number/IRMMZD6HYA6FSHHTDLGMOG2QYL/graph.json","fetch_events":"https://pith.science/api/pith-number/IRMMZD6HYA6FSHHTDLGMOG2QYL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IRMMZD6HYA6FSHHTDLGMOG2QYL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IRMMZD6HYA6FSHHTDLGMOG2QYL/action/storage_attestation","attest_author":"https://pith.science/pith/IRMMZD6HYA6FSHHTDLGMOG2QYL/action/author_attestation","sign_citation":"https://pith.science/pith/IRMMZD6HYA6FSHHTDLGMOG2QYL/action/citation_signature","submit_replication":"https://pith.science/pith/IRMMZD6HYA6FSHHTDLGMOG2QYL/action/replication_record"}},"created_at":"2026-05-18T00:05:55.282501+00:00","updated_at":"2026-05-18T00:05:55.282501+00:00"}