On totally ramified extensions of discrete valued fields
classification
🧮 math.NT
math.RA
keywords
criterionfieldsramifiedtotallyvaluationsapplyartin-schreiercharacteristic
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We give a simple characterization of the totally wild ramified valuations in a Galois extension of fields of characteristic p. This criterion involves the valuations of Artin-Schreier cosets of the F_{p^r}^\times-translation of a single element. We apply the criterion to construct some interesting examples.
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