Axiomatizing the existential theory of Fq((t))
Logic
2023-10-04 v4 Number Theory
Abstract
We study the existential theory of equicharacteristic henselian valued fields with a distinguished uniformizer. In particular, assuming a weak consequence of resolution of singularities, we obtain an axiomatization of - and therefore an algorithm to decide - the existential theory relative to the existential theory of the residue field. This is both more general and works under weaker resolution hypotheses than the algorithm of Denef and Schoutens, which we also discuss in detail. In fact, the consequence of resolution of singularities our results are conditional on is the weakest under which they hold true.
Keywords
Cite
@article{arxiv.2205.05438,
title = {Axiomatizing the existential theory of Fq((t))},
author = {Sylvy Anscombe and Philip Dittmann and Arno Fehm},
journal= {arXiv preprint arXiv:2205.05438},
year = {2023}
}
Comments
New Remark 4.18 and expanded Remark 2.4