English

Definable henselian valuations in positive residue characteristic

Logic 2025-11-12 v3 Commutative Algebra

Abstract

We study the question of Lring\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.

Keywords

Cite

@article{arxiv.2401.06884,
  title  = {Definable henselian valuations in positive residue characteristic},
  author = {Margarete Ketelsen and Simone Ramello and Piotr Szewczyk},
  journal= {arXiv preprint arXiv:2401.06884},
  year   = {2025}
}

Comments

23 pages, 3 figures; minor fixes, in particular in section 6; changed numbering to match published version