AKE principles for deeply ramified fields
Logic
2026-04-01 v1 Commutative Algebra
Abstract
We study the model theory of deeply ramified fields of positive characteristic. Generalizing the perfect case treated in work by Jahnke and Kartas on the model theory of perfectoid fields, we obtain Ax-Kochen/Ershov principles for certain deeply ramified fields of positive characteristic and fixed degree of imperfection. Our results apply in particular to all deeply ramified henselian valued fields of rank 1.
Keywords
Cite
@article{arxiv.2603.29528,
title = {AKE principles for deeply ramified fields},
author = {Franziska Jahnke and Jonas van der Schaaf},
journal= {arXiv preprint arXiv:2603.29528},
year = {2026}
}