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We show the analogous statement for the Abel map X/\\partial X -> Picbar (X/\\partial X) to the compactified Picard, or Jacobian, scheme, namely this map realizes the Poincar\\'e duality isomorphism H_1(X/ \\partial X, Z/n) -> H^1(X, Z/n(1)). In particular, H_1 of this Abel map is an isomorphism.\n  In proving this result, we prove some results about P","authors_text":"Jesse Leo Kass, Kirsten Wickelgren","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-05-27T21:16:58Z","title":"An Abel map to the compactified Picard scheme realizes Poincar\\'e duality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6330","kind":"arxiv","version":2},"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":"sha256:36c253d4bae89e322b1e537022d847bd2426ca3db37ab0f7698384b693f57929","target":"record","created_at":"2026-05-18T02:03:38Z","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":"d3741284aa07a4e7487ff12f9853c7f44589bd8a7ff0a78abe0440be6a9a028a","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-05-27T21:16:58Z","title_canon_sha256":"d5bfbe3340608274d12b42c189c453ea605bb1e6d61a5a3fd4b9084c4c234bd2"},"schema_version":"1.0","source":{"id":"1305.6330","kind":"arxiv","version":2}},"canonical_sha256":"ffa4053a13b070ee1b671b5f97dd041edddbf94e22a787418dbf81512107f9f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ffa4053a13b070ee1b671b5f97dd041edddbf94e22a787418dbf81512107f9f9","first_computed_at":"2026-05-18T02:03:38.277996Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:38.277996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t/bhNh7FPZeL7hcmF8EcOsNErOPoDD8ZJtNEssOHSziX+RwMocFq+xziFU1FXeW8ywUlxGPswWEjWC2lPIQJCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:38.278646Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.6330","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36c253d4bae89e322b1e537022d847bd2426ca3db37ab0f7698384b693f57929","sha256:8380b7cfe58726192a1fb616da47aa90be23eee6623e0bf5079914540d849d75"],"state_sha256":"f344b2c0d12ae280a537c2bdb3740c7521a102333f5a7b877af890fa5f5761a4"}