Ramification of valuations |
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Authors: | Steven Dale Cutkosky Olivier Piltant |
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Affiliation: | a Department of Mathematics, University of Missouri, Columbia, MO 65211, USA b LAMA-UMR 8100 du CNRS, Université de Versailles, 45, avenue des Etats-Unis, Bâtiment Fermat, 78035 Versailles, France |
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Abstract: | In this paper we develop a very explicit theory of ramification of general valuations in algebraic function fields. In characteristic zero and arbitrary dimension, we obtain the strongest possible generalization of the classical ramification theory of local Dedekind domains. We further develop a ramification theory of algebraic functions fields of dimension two in positive characteristic. We prove that local monomialization and simultaneous resolution hold under very mild assumptions, and give pathological examples. |
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Keywords: | Ramification Valuation Resolution of singularities Characteristic p |
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