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arXiv · 2506.13742

A note on valued fields with finite group actions

Piotr Błaszkiewicz·Jakub Gogolok
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Abstract

We consider valued fields equipped with an action of a given finite group by automorphisms. We show that the theory of such structures admits a model companion which is axiomatized in an Ax-Kochen/Ershov fashion. We prove this model companion has $\operatorname{NTP}_2$ and that the valuation is definable in the pure field language.

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Piotr Błaszkiewicz, Jakub Gogolok. 2025-06-16. A note on valued fields with finite group actions. https://arxiv.org/abs/2506.13742

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