{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:GZXCBTAIG6ARIC5IUMBYD47VXM","short_pith_number":"pith:GZXCBTAI","schema_version":"1.0","canonical_sha256":"366e20cc083781140ba8a30381f3f5bb3221104a82abc7aaa7834d9031d4e976","source":{"kind":"arxiv","id":"1505.04049","version":1},"attestation_state":"computed","paper":{"title":"Deformations of algebras defined by tilting bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.AG","authors_text":"Joseph Karmazyn","submitted_at":"2015-05-15T12:33:08Z","abstract_excerpt":"In this paper we produce noncommutative algebras derived equivalent to deformations of schemes with tilting bundles. We do this in two settings, first proving that a tilting bundle on a scheme lifts to a tilting bundle on an infinitesimal deformations of that scheme and then expanding this result to $\\mathbb{C}^*$-equivariant deformations over schemes with a good $\\mathbb{C}^*$-action. In both these situations the endomorphism algebra of the lifted tilting bundle produces a deformation of the original endomorphism algebra, and this is a graded deformation in the $\\mathbb{C}^*$-equivariant case"},"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":"1505.04049","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-05-15T12:33:08Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"7843886112f3c4349c1b1176abb43dbb2ede491c967e97d666621b2cce8cb73c","abstract_canon_sha256":"9f741e73921d4acbc0075696df146d48b28e27649e2f4e04505f27822292dfa6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:09:40.312777Z","signature_b64":"PsqXVBYS89NZAbs17WnXhuG5366qJgXbLbeq96Ds+E3L+Zb/VeU7mduOLn2TQtITpc6dsbGackEywmxFbvEyCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"366e20cc083781140ba8a30381f3f5bb3221104a82abc7aaa7834d9031d4e976","last_reissued_at":"2026-05-18T02:09:40.311433Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:09:40.311433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Deformations of algebras defined by tilting bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.AG","authors_text":"Joseph Karmazyn","submitted_at":"2015-05-15T12:33:08Z","abstract_excerpt":"In this paper we produce noncommutative algebras derived equivalent to deformations of schemes with tilting bundles. We do this in two settings, first proving that a tilting bundle on a scheme lifts to a tilting bundle on an infinitesimal deformations of that scheme and then expanding this result to $\\mathbb{C}^*$-equivariant deformations over schemes with a good $\\mathbb{C}^*$-action. In both these situations the endomorphism algebra of the lifted tilting bundle produces a deformation of the original endomorphism algebra, and this is a graded deformation in the $\\mathbb{C}^*$-equivariant case"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04049","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":"1505.04049","created_at":"2026-05-18T02:09:40.311824+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.04049v1","created_at":"2026-05-18T02:09:40.311824+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.04049","created_at":"2026-05-18T02:09:40.311824+00:00"},{"alias_kind":"pith_short_12","alias_value":"GZXCBTAIG6AR","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"GZXCBTAIG6ARIC5I","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"GZXCBTAI","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/GZXCBTAIG6ARIC5IUMBYD47VXM","json":"https://pith.science/pith/GZXCBTAIG6ARIC5IUMBYD47VXM.json","graph_json":"https://pith.science/api/pith-number/GZXCBTAIG6ARIC5IUMBYD47VXM/graph.json","events_json":"https://pith.science/api/pith-number/GZXCBTAIG6ARIC5IUMBYD47VXM/events.json","paper":"https://pith.science/paper/GZXCBTAI"},"agent_actions":{"view_html":"https://pith.science/pith/GZXCBTAIG6ARIC5IUMBYD47VXM","download_json":"https://pith.science/pith/GZXCBTAIG6ARIC5IUMBYD47VXM.json","view_paper":"https://pith.science/paper/GZXCBTAI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.04049&json=true","fetch_graph":"https://pith.science/api/pith-number/GZXCBTAIG6ARIC5IUMBYD47VXM/graph.json","fetch_events":"https://pith.science/api/pith-number/GZXCBTAIG6ARIC5IUMBYD47VXM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GZXCBTAIG6ARIC5IUMBYD47VXM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GZXCBTAIG6ARIC5IUMBYD47VXM/action/storage_attestation","attest_author":"https://pith.science/pith/GZXCBTAIG6ARIC5IUMBYD47VXM/action/author_attestation","sign_citation":"https://pith.science/pith/GZXCBTAIG6ARIC5IUMBYD47VXM/action/citation_signature","submit_replication":"https://pith.science/pith/GZXCBTAIG6ARIC5IUMBYD47VXM/action/replication_record"}},"created_at":"2026-05-18T02:09:40.311824+00:00","updated_at":"2026-05-18T02:09:40.311824+00:00"}