{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:QS32L47ET4HTIHCVAVG6MZR3W2","short_pith_number":"pith:QS32L47E","schema_version":"1.0","canonical_sha256":"84b7a5f3e49f0f341c55054de6663bb6883e3b2c0117f570b691997626faf3a7","source":{"kind":"arxiv","id":"1305.4687","version":2},"attestation_state":"computed","paper":{"title":"From semi-orthogonal decompositions to polarized intermediate Jacobians via Jacobians of noncommutative motives","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.KT"],"primary_cat":"math.AG","authors_text":"Goncalo Tabuada, Marcello Bernardara","submitted_at":"2013-05-21T01:10:56Z","abstract_excerpt":"Let X and Y be complex smooth projective varieties, and D^b(X) and D^b(Y) the associated bounded derived categories of coherent sheaves. Assume the existence of a triangulated category T which is admissible both in D^b(X) as in D^b(Y). Making use of the recent theory of Jacobians of noncommutative motives, we construct out of this categorical data a morphism t of abelian varieties (up to isogeny) from the product of the intermediate algebraic Jacobians of X to the product of the intermediate algebraic Jacobians of Y. When the orthogonal complement of T in D^b(X) has a trivial Jacobian (e.g. wh"},"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":"1305.4687","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-05-21T01:10:56Z","cross_cats_sorted":["math.AT","math.KT"],"title_canon_sha256":"2a596c8c8fe705f2a19e9f8558b89cd39d0b0de7bee7bff94f2da950cf0ba148","abstract_canon_sha256":"f769eeec75da26da504d9efaf19cbfa0cc8a7dd1e837ce4446a76b657ed39dff"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:59.687086Z","signature_b64":"7jsSsEmwRO0etnCCL1nPysJ45Za7RKWUm8+CiiD0YAIprNVzBDcmC2DYPAM7A7RE69zWzRbEVRUW+Aahdc+5Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"84b7a5f3e49f0f341c55054de6663bb6883e3b2c0117f570b691997626faf3a7","last_reissued_at":"2026-05-18T02:50:59.686557Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:59.686557Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"From semi-orthogonal decompositions to polarized intermediate Jacobians via Jacobians of noncommutative motives","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.KT"],"primary_cat":"math.AG","authors_text":"Goncalo Tabuada, Marcello Bernardara","submitted_at":"2013-05-21T01:10:56Z","abstract_excerpt":"Let X and Y be complex smooth projective varieties, and D^b(X) and D^b(Y) the associated bounded derived categories of coherent sheaves. Assume the existence of a triangulated category T which is admissible both in D^b(X) as in D^b(Y). Making use of the recent theory of Jacobians of noncommutative motives, we construct out of this categorical data a morphism t of abelian varieties (up to isogeny) from the product of the intermediate algebraic Jacobians of X to the product of the intermediate algebraic Jacobians of Y. When the orthogonal complement of T in D^b(X) has a trivial Jacobian (e.g. wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.4687","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":"1305.4687","created_at":"2026-05-18T02:50:59.686643+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.4687v2","created_at":"2026-05-18T02:50:59.686643+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.4687","created_at":"2026-05-18T02:50:59.686643+00:00"},{"alias_kind":"pith_short_12","alias_value":"QS32L47ET4HT","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_16","alias_value":"QS32L47ET4HTIHCV","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_8","alias_value":"QS32L47E","created_at":"2026-05-18T12:27:57.521954+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/QS32L47ET4HTIHCVAVG6MZR3W2","json":"https://pith.science/pith/QS32L47ET4HTIHCVAVG6MZR3W2.json","graph_json":"https://pith.science/api/pith-number/QS32L47ET4HTIHCVAVG6MZR3W2/graph.json","events_json":"https://pith.science/api/pith-number/QS32L47ET4HTIHCVAVG6MZR3W2/events.json","paper":"https://pith.science/paper/QS32L47E"},"agent_actions":{"view_html":"https://pith.science/pith/QS32L47ET4HTIHCVAVG6MZR3W2","download_json":"https://pith.science/pith/QS32L47ET4HTIHCVAVG6MZR3W2.json","view_paper":"https://pith.science/paper/QS32L47E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.4687&json=true","fetch_graph":"https://pith.science/api/pith-number/QS32L47ET4HTIHCVAVG6MZR3W2/graph.json","fetch_events":"https://pith.science/api/pith-number/QS32L47ET4HTIHCVAVG6MZR3W2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QS32L47ET4HTIHCVAVG6MZR3W2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QS32L47ET4HTIHCVAVG6MZR3W2/action/storage_attestation","attest_author":"https://pith.science/pith/QS32L47ET4HTIHCVAVG6MZR3W2/action/author_attestation","sign_citation":"https://pith.science/pith/QS32L47ET4HTIHCVAVG6MZR3W2/action/citation_signature","submit_replication":"https://pith.science/pith/QS32L47ET4HTIHCVAVG6MZR3W2/action/replication_record"}},"created_at":"2026-05-18T02:50:59.686643+00:00","updated_at":"2026-05-18T02:50:59.686643+00:00"}