The relative approximation degree in valued function fields |
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Authors: | Franz-Viktor Kuhlmann Izabela Vlahu |
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Affiliation: | 1. Department of Mathematics and Statistics, University of Saskatchewan, 106 Wiggins Road, Saskatoon, Saskatchewan, S7N 5E6, Canada
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Abstract: | We continue the work of Kaplansky on immediate valued field extensions and determine special properties of elements in such extensions. In particular, we are interested in the question when an immediate valued function field of transcendence degree 1 is henselian rational (i.e., generated, modulo henselization, by one element). If so, then ramification can be eliminated in this valued function field. The results presented in this paper are crucial for the first author’s proof of henselian rationality over tame fields, which in turn is used in his work on local uniformization. |
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