{"paper":{"title":"Toroidalization of generating sequences in dimension two function fields","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Huy Tai Ha, Laura Ghezzi, Olga Kashcheyeva","submitted_at":"2005-09-29T14:54:09Z","abstract_excerpt":"Let k be an algebraically closed field of characteristic 0 and let K*/K be a finite extension of algebraic function fields of transcendence degree 2 over k. Let v* be a k-valuation of K* with valuation ring V* and let v be the restriction of v* to K. Suppose R --> S is an extension of algebraic regular local rings with quotient fields K and K*, respectively, such that V* dominates S and S dominates R. We prove that there exist sequences of quadratic transforms R --> R' and S --> S' along v* such that S' dominates R' and the map between generating sequences of v and v* in R' and S', respectivel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0509697","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"}