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arXiv · 2601.04872

On algebraically maximal valued fields that are not defectless

Franz-Viktor Kuhlmann
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Abstract

An example originally given by F.~Delon shows the existence of an algebraically maximal discretely valued field of characteristic $p>0$ which admits purely inseparable extensions of degree $p^2$ with defect $p$. These extensions are not generated by a single element. Using a trick introduced in an earlier paper of the author, we construct algebraically maximal valued fields, of characteristic $p$ as well as of characteristic $0$, which admit separable extensions of degree $p^2$ with defect $p$. They are of rank 2 and it is an open question whether such examples having rank 1 exist.

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Franz-Viktor Kuhlmann. 2026-01-08. On algebraically maximal valued fields that are not defectless. https://arxiv.org/abs/2601.04872

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