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.
From: Franz-Viktor Kuhlmann [view email]
[v1]
Thu, 8 Jan 2026 12:18:11 UTC (9 KB)
[v2]
Tue, 2 Jun 2026 08:18:17 UTC (8 KB)
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