Local Uniformization of Abhyankar Valuations

DOI10.1307/MMJ/20205888arXiv2003.06374MaRDI QIDQ6336716

Publication date: 13 March 2020

Abstract: We prove local uniformization of Abhyankar valuations of an algebraic function field K over a ground field k. Our result generalizes the proof of this result, with the additional assumption that the residue field of the valuation ring is separable over k, by Hagen Knaf and Franz-Viktor Kuhlmann. The proof in this paper uses different methods, being inspired by the approach of Zariski and Abhyankar.

Mathematics Subject Classification ID

Global theory and resolution of singularities (algebro-geometric aspects) (14E15) Valuations and their generalizations for commutative rings (13A18) Regular local rings (13H05)

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