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arXiv · 2606.01310

Large imperfect fields are existentially closed in function fields after finite constant extension

Hagen Knaf·Franz-Viktor Kuhlmann
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Abstract

For an algebraic function field $F$ over a large field $K$, we show: 1) if $F|K$ has a rational place, then there is a finite purely inseparable extension $K'|K$ such that $K'$ is existentially closed in $F.K'$; 2) $F|K$ has a rational place admitting local uniformization if and only if $K$ is existentially closed in $F$.

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Hagen Knaf, Franz-Viktor Kuhlmann. 2026-05-31. Large imperfect fields are existentially closed in function fields after finite constant extension. https://arxiv.org/abs/2606.01310

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