{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:2OD7RZ5D3EKZE2KHUUNJMGZLAD","short_pith_number":"pith:2OD7RZ5D","schema_version":"1.0","canonical_sha256":"d387f8e7a3d915926947a51a961b2b00dec39bc1fe4b80c40cba2ffcd5d1cd93","source":{"kind":"arxiv","id":"0711.1734","version":2},"attestation_state":"computed","paper":{"title":"Base change for semiorthogonal decompositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AG","authors_text":"Alexander Kuznetsov","submitted_at":"2007-11-12T10:25:30Z","abstract_excerpt":"Consider an algebraic variety $X$ over a base scheme $S$ and a faithful base change $T \\to S$. Given an admissible subcategory $\\CA$ in the bounded derived category of coherent sheaves on $X$, we construct an admissible subcategory in the bounded derived category of coherent sheaves on the fiber product $X\\times_S T$, called the base change of $\\CA$, in such a way that the following base change theorem holds: if a semiorthogonal decomposition of the bounded derived category of $X$ is given then the base changes of its components form a semiorthogonal decomposition of the bounded derived catego"},"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":"0711.1734","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-11-12T10:25:30Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"e89488d43111cfebcefa309bc60fd4a9e0ae6afb8adcfc5aa7ffae4f2beb2550","abstract_canon_sha256":"4b2dd8eda82e73ebf2a23f15f62c305cbd3ddfea866a1f4ad0335b19f7b8ece3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:16.578385Z","signature_b64":"kjoXlraXBAWdM06n6eX2EfWxzp2JoWFgSQy9GKvMJjy0YB660ZW2VxvYV/8v66i15p6byupvRdgYxXvQia9zCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d387f8e7a3d915926947a51a961b2b00dec39bc1fe4b80c40cba2ffcd5d1cd93","last_reissued_at":"2026-05-18T00:06:16.577691Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:16.577691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Base change for semiorthogonal decompositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AG","authors_text":"Alexander Kuznetsov","submitted_at":"2007-11-12T10:25:30Z","abstract_excerpt":"Consider an algebraic variety $X$ over a base scheme $S$ and a faithful base change $T \\to S$. Given an admissible subcategory $\\CA$ in the bounded derived category of coherent sheaves on $X$, we construct an admissible subcategory in the bounded derived category of coherent sheaves on the fiber product $X\\times_S T$, called the base change of $\\CA$, in such a way that the following base change theorem holds: if a semiorthogonal decomposition of the bounded derived category of $X$ is given then the base changes of its components form a semiorthogonal decomposition of the bounded derived catego"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.1734","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":""},"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":"0711.1734","created_at":"2026-05-18T00:06:16.577786+00:00"},{"alias_kind":"arxiv_version","alias_value":"0711.1734v2","created_at":"2026-05-18T00:06:16.577786+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0711.1734","created_at":"2026-05-18T00:06:16.577786+00:00"},{"alias_kind":"pith_short_12","alias_value":"2OD7RZ5D3EKZ","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"2OD7RZ5D3EKZE2KH","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"2OD7RZ5D","created_at":"2026-05-18T12:25:54.717736+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2312.06930","citing_title":"The Lichtenbaum-Quillen dimension of complex varieties","ref_index":63,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2OD7RZ5D3EKZE2KHUUNJMGZLAD","json":"https://pith.science/pith/2OD7RZ5D3EKZE2KHUUNJMGZLAD.json","graph_json":"https://pith.science/api/pith-number/2OD7RZ5D3EKZE2KHUUNJMGZLAD/graph.json","events_json":"https://pith.science/api/pith-number/2OD7RZ5D3EKZE2KHUUNJMGZLAD/events.json","paper":"https://pith.science/paper/2OD7RZ5D"},"agent_actions":{"view_html":"https://pith.science/pith/2OD7RZ5D3EKZE2KHUUNJMGZLAD","download_json":"https://pith.science/pith/2OD7RZ5D3EKZE2KHUUNJMGZLAD.json","view_paper":"https://pith.science/paper/2OD7RZ5D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0711.1734&json=true","fetch_graph":"https://pith.science/api/pith-number/2OD7RZ5D3EKZE2KHUUNJMGZLAD/graph.json","fetch_events":"https://pith.science/api/pith-number/2OD7RZ5D3EKZE2KHUUNJMGZLAD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2OD7RZ5D3EKZE2KHUUNJMGZLAD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2OD7RZ5D3EKZE2KHUUNJMGZLAD/action/storage_attestation","attest_author":"https://pith.science/pith/2OD7RZ5D3EKZE2KHUUNJMGZLAD/action/author_attestation","sign_citation":"https://pith.science/pith/2OD7RZ5D3EKZE2KHUUNJMGZLAD/action/citation_signature","submit_replication":"https://pith.science/pith/2OD7RZ5D3EKZE2KHUUNJMGZLAD/action/replication_record"}},"created_at":"2026-05-18T00:06:16.577786+00:00","updated_at":"2026-05-18T00:06:16.577786+00:00"}