Abhyankar places admit local uniformization in any characteristic

@inproceedings{Knaf2001AbhyankarPA,
  title={Abhyankar places admit local uniformization in any characteristic},
  author={Hagen Knaf and Franz Kuhlmann},
  year={2001}
}
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 ⊆ K of Krull dimension dimR ≤ 2, assuming that the valued field (K, vP ) is defectless… CONTINUE READING
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