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arXiv · 2401.06884

Definable henselian valuations in positive residue characteristic

Margarete Ketelsen·Simone Ramello·Piotr Szewczyk
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Abstract

We study the question of $\mathcal{L}_{\mathrm{ring}}$-definability of non-trivial henselian valuation rings. Building on previous work of Jahnke and Koenigsmann, we provide a characterization of henselian fields that admit a non-trivial definable henselian valuation. In particular, we treat cases where the canonical henselian valuation has positive residue characteristic, using techniques from the model theory and algebra of tame fields.

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Margarete Ketelsen, Simone Ramello, Piotr Szewczyk. 2024-01-12. Definable henselian valuations in positive residue characteristic. https://doi.org/10.1017/jsl.2024.55

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