{"paper":{"title":"Abhyankar places admit local uniformization in any characteristic","license":"","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Franz-Viktor Kuhlmann, Hagen Knaf","submitted_at":"2003-04-12T23:35:40Z","abstract_excerpt":"We prove that every place $P$ of an algebraic function field $F|K$ of arbitrary characteristic admits local uniformization, provided that the sum of the rational rank of its value group and the transcendence degree of its residue field $FP$ over $K$ is equal to the transcendence degree of $F|K$, and the extension $FP|K$ is separable. We generalize this result to the case where $P$ dominates a regular local Nagata ring $R\\subseteq K$ of Krull dimension $\\dim R\\leq 2$, assuming that the valued field $(K,v_P)$ is defectless, the factor group $v_P F/v_P K$ is torsion-free and the extension of resi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0304159","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"}