{"paper":{"title":"An Abel map to the compactified Picard scheme realizes Poincar\\'e duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.AG","authors_text":"Jesse Leo Kass, Kirsten Wickelgren","submitted_at":"2013-05-27T21:16:58Z","abstract_excerpt":"For a smooth algebraic curve X over a field, applying H_1 to the Abel map X -> Pic (X/\\partial X) to the Picard scheme of X modulo its boundary realizes the Poincar\\'e duality isomorphism H_1(X, Z/ n) -> H^1(X/ \\partial X, Z/n(1)) = H^1_c(X, Z/n(1)). 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6330","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"}