Characterizing diophantine henselian valuation rings and valuation ideals
Logic
2017-05-24 v1 Commutative Algebra
Number Theory
Abstract
We give a characterization, in terms of the residue field, of those henselian valuation rings and those henselian valuation ideals that are diophantine. This characterization gives a common generalization of all the positive and negative results on diophantine henselian valuation rings and diophantine valuation ideals in the literature. We also treat questions of uniformity and we apply the results to show that a given field can carry at most one diophantine nontrivial equicharacteristic henselian valuation ring or valuation ideal.
Keywords
Cite
@article{arxiv.1602.01233,
title = {Characterizing diophantine henselian valuation rings and valuation ideals},
author = {Sylvy Anscombe and Arno Fehm},
journal= {arXiv preprint arXiv:1602.01233},
year = {2017}
}
Comments
29 pages