{"paper":{"title":"Dimension filtrations in birational localisation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"David Kumallagov","submitted_at":"2026-06-27T18:43:47Z","abstract_excerpt":"Let \\(S_b\\) be the class of birational morphisms between smooth varieties over a field \\(F\\), and let \\(L_n=S_b^{-1}d_{\\leq n}\\Sm(F)\\). Kahn and Sujatha asked whether the natural functor \\(L_n\\to S_b^{-1}\\Sm(F)\\) is fully faithful. We prove that it is fully faithful exactly for \\(n=0\\). More strongly, for every \\(n\\geq1\\) and every \\(N\\geq n+1\\), the transition functor \\(L_n\\to L_N\\) has an infinite fibre on an endomorphism set. The proof identifies a sharp dimension threshold: if \\(\\dim X+r\\leq n\\), then \\(X\\times\\mathbb A^r\\to X\\) is invertible in \\(L_n\\) precisely when \\(\\dim X+r\\leq n-1\\)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.29044","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.29044/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}