Definable henselian valuations in positive residue characteristic
Logic
2025-11-12 v3 Commutative Algebra
Abstract
We study the question of -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