Differential-henselianity and maximality of asymptotic valued differential fields
Commutative Algebra
2020-12-09 v5 Logic
Abstract
We show that asymptotic (valued differential) fields have unique maximal immediate extensions. Connecting this to differential-henselianity, we prove that any differential-henselian asymptotic field is differential-algebraically maximal, removing the assumption of monotonicity from a theorem of Aschenbrenner, van den Dries, and van der Hoeven (arXiv:1509.02588, Theorem 7.0.3). Finally, we use this result to show the existence and uniqueness of differential-henselizations of asymptotic fields.
Keywords
Cite
@article{arxiv.1805.05890,
title = {Differential-henselianity and maximality of asymptotic valued differential fields},
author = {Nigel Pynn-Coates},
journal= {arXiv preprint arXiv:1805.05890},
year = {2020}
}
Comments
31 pages; v5: minor corrections and clarifications made throughout