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arXiv · 2101.04707

Valued fields with finitely many defect extensions of prime degree

Franz-Viktor Kuhlmann
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Abstract

We prove that a valued field of positive characteristic $p$ that has only finitely many distinct Artin-Schreier extensions (which is a property of infinite NTP$_2$ fields) is dense in its perfect hull. As a consequence, it is a deeply ramified field and has $p$-divisible value group and perfect residue field. Further, we prove a partial analogue for valued fields of mixed characteristic and observe an open problem about 1-units in this setting. Finally, we fill a gap that occurred in a proof in an earlier paper in which we first introduced a classification of Artin-Schreier defect extensions.

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Franz-Viktor Kuhlmann. 2021-01-12. Valued fields with finitely many defect extensions of prime degree. https://doi.org/10.1142/s0219498822500499

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