{"paper":{"title":"The membership problem for polynomial ideals in terms of residue currents","license":"","headline":"","cross_cats":["math.AC","math.AG"],"primary_cat":"math.CV","authors_text":"Mats Andersson","submitted_at":"2005-03-14T13:09:15Z","abstract_excerpt":"We find a relation between the vanishing of a globally defined residue current on $\\P^n$ and solution of the membership problem with control of the polynomial degrees. Several classical results appear as special cases, such as Max N\\\"other's theorem, and we also obtain a generalization of that theorem. There are also connections to effective versions of the Nullstellensatz. We also provide explicit integral representations of the solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0503259","kind":"arxiv","version":1},"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"}