{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:QXVYBX3K7SJVUIZUH2XT56X5DN","short_pith_number":"pith:QXVYBX3K","schema_version":"1.0","canonical_sha256":"85eb80df6afc935a23343eaf3efafd1b79dc7edbcf6b7a13c501323b81d20090","source":{"kind":"arxiv","id":"0902.2533","version":3},"attestation_state":"computed","paper":{"title":"Albanese varieties with modulus over a perfect field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Henrik Russell","submitted_at":"2009-02-15T09:29:09Z","abstract_excerpt":"Let X be a smooth proper variety over a perfect field k of arbitrary characteristic. Let D be an effective divisor on X with multiplicity. We introduce an Albanese variety Alb(X, D) of X of modulus D as a higher dimensional analogon of the generalized Jacobian of Rosenlicht-Serre with modulus for smooth proper curves. Basing on duality of 1-motives with unipotent part (which are introduced here), we obtain explicit and functorial descriptions of these generalized Albanese varieties and their dual functors.\n  We define a relative Chow group of zero cycles w.r.t. the modulus D and show that Alb("},"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":"0902.2533","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-02-15T09:29:09Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"413d81bc30317a2f43abb2c1e8f1a8b4448fb03e4c692c625c0bdceb14819a3e","abstract_canon_sha256":"ac7b5748bb8438e3e5abe8825a0d685ac60820a2c918414147989329a1dadc7b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:10.063724Z","signature_b64":"E74IagpfUxYBMV+onbmxCzVp+B/RpqnQNB5biHbzAGrv7et8av6bp/SZAog/UpbEOZRqMQ70MfbK22CthfblBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85eb80df6afc935a23343eaf3efafd1b79dc7edbcf6b7a13c501323b81d20090","last_reissued_at":"2026-05-18T03:11:10.063211Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:10.063211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Albanese varieties with modulus over a perfect field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Henrik Russell","submitted_at":"2009-02-15T09:29:09Z","abstract_excerpt":"Let X be a smooth proper variety over a perfect field k of arbitrary characteristic. Let D be an effective divisor on X with multiplicity. We introduce an Albanese variety Alb(X, D) of X of modulus D as a higher dimensional analogon of the generalized Jacobian of Rosenlicht-Serre with modulus for smooth proper curves. Basing on duality of 1-motives with unipotent part (which are introduced here), we obtain explicit and functorial descriptions of these generalized Albanese varieties and their dual functors.\n  We define a relative Chow group of zero cycles w.r.t. the modulus D and show that Alb("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.2533","kind":"arxiv","version":3},"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":"0902.2533","created_at":"2026-05-18T03:11:10.063284+00:00"},{"alias_kind":"arxiv_version","alias_value":"0902.2533v3","created_at":"2026-05-18T03:11:10.063284+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.2533","created_at":"2026-05-18T03:11:10.063284+00:00"},{"alias_kind":"pith_short_12","alias_value":"QXVYBX3K7SJV","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_16","alias_value":"QXVYBX3K7SJVUIZU","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_8","alias_value":"QXVYBX3K","created_at":"2026-05-18T12:26:01.383474+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/QXVYBX3K7SJVUIZUH2XT56X5DN","json":"https://pith.science/pith/QXVYBX3K7SJVUIZUH2XT56X5DN.json","graph_json":"https://pith.science/api/pith-number/QXVYBX3K7SJVUIZUH2XT56X5DN/graph.json","events_json":"https://pith.science/api/pith-number/QXVYBX3K7SJVUIZUH2XT56X5DN/events.json","paper":"https://pith.science/paper/QXVYBX3K"},"agent_actions":{"view_html":"https://pith.science/pith/QXVYBX3K7SJVUIZUH2XT56X5DN","download_json":"https://pith.science/pith/QXVYBX3K7SJVUIZUH2XT56X5DN.json","view_paper":"https://pith.science/paper/QXVYBX3K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0902.2533&json=true","fetch_graph":"https://pith.science/api/pith-number/QXVYBX3K7SJVUIZUH2XT56X5DN/graph.json","fetch_events":"https://pith.science/api/pith-number/QXVYBX3K7SJVUIZUH2XT56X5DN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QXVYBX3K7SJVUIZUH2XT56X5DN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QXVYBX3K7SJVUIZUH2XT56X5DN/action/storage_attestation","attest_author":"https://pith.science/pith/QXVYBX3K7SJVUIZUH2XT56X5DN/action/author_attestation","sign_citation":"https://pith.science/pith/QXVYBX3K7SJVUIZUH2XT56X5DN/action/citation_signature","submit_replication":"https://pith.science/pith/QXVYBX3K7SJVUIZUH2XT56X5DN/action/replication_record"}},"created_at":"2026-05-18T03:11:10.063284+00:00","updated_at":"2026-05-18T03:11:10.063284+00:00"}