{"paper":{"title":"Coleff-Herrera currents, duality, and Noetherian operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Mats Andersson","submitted_at":"2009-02-18T07:44:31Z","abstract_excerpt":"Let $\\I$ be a coherent subsheaf of a locally free sheaf $\\Ok(E_0)$ and suppose that $\\F=\\Ok(E_0)/\\I$ has pure codimension. Starting with a residue current $R$ obtained from a locally free resolution of $\\F$ we construct a vector-valued Coleff-Herrera current $\\mu$ with support on the variety associated to $\\F$ such that $\\phi$ is in $\\I$ if and only if $\\mu\\phi=0$. Such a current $\\mu$ can also be derived algebraically from a fundamental theorem of Roos about the bidualizing functor, and the relation between these two approaches is discussed. By a construction due to Bj\\\"ork one gets Noetheria"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.3064","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"}