{"paper":{"title":"How to construct a closed subscheme, or a coherent subsheaf, with prescribed germs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Nitin Nitsure","submitted_at":"2014-12-15T14:14:05Z","abstract_excerpt":"We show that a closed subscheme of a given locally noetherian scheme can be constructed by prescribing it germs at all points of the ambient scheme in a manner consistent with specialization of points, provided the resulting set of all associated points of all the germs is locally finite. More generally, we prove a similar result for constructing a coherent subsheaf of a coherent sheaf by prescribing its stalks at all points in a manner consistent with specializations of points, again provided the set of all associated points of all the corresponding local quotients is locally finite.\n  On any"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.4600","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"}