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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(","authors_text":"Henrik Russell","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-02-15T09:29:09Z","title":"Albanese varieties with modulus over a perfect field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.2533","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:315f040baf4e928e6eaf271252697dfd4543afbde9f4f0c76b5f8305c79aef47","target":"record","created_at":"2026-05-18T03:11:10Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ac7b5748bb8438e3e5abe8825a0d685ac60820a2c918414147989329a1dadc7b","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-02-15T09:29:09Z","title_canon_sha256":"413d81bc30317a2f43abb2c1e8f1a8b4448fb03e4c692c625c0bdceb14819a3e"},"schema_version":"1.0","source":{"id":"0902.2533","kind":"arxiv","version":3}},"canonical_sha256":"85eb80df6afc935a23343eaf3efafd1b79dc7edbcf6b7a13c501323b81d20090","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85eb80df6afc935a23343eaf3efafd1b79dc7edbcf6b7a13c501323b81d20090","first_computed_at":"2026-05-18T03:11:10.063211Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:10.063211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E74IagpfUxYBMV+onbmxCzVp+B/RpqnQNB5biHbzAGrv7et8av6bp/SZAog/UpbEOZRqMQ70MfbK22CthfblBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:10.063724Z","signed_message":"canonical_sha256_bytes"},"source_id":"0902.2533","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:315f040baf4e928e6eaf271252697dfd4543afbde9f4f0c76b5f8305c79aef47","sha256:bbefc4d5a6bd7c6859b49f7f0215846a849df72f6b1bf2394e29d48d10b06424"],"state_sha256":"d0f5aab767dcb87b24b31f162cf520eede17f610bf41b880d37a1ebd423198bb"}