Undecidability in function fields of positive characteristic
Number Theory
2008-02-27 v2 Logic
Abstract
We prove that the first-order theory of any function field K of characteristic p>2 is undecidable in the language of rings without parameters. When K is a function field in one variable whose constant field is algebraic over a finite field, we can also prove undecidability in characteristic 2. The proof uses a result by Moret-Bailly about ranks of elliptic curves over function fields.
Keywords
Cite
@article{arxiv.0709.1739,
title = {Undecidability in function fields of positive characteristic},
author = {Kirsten Eisentraeger and Alexandra Shlapentokh},
journal= {arXiv preprint arXiv:0709.1739},
year = {2008}
}
Comments
12 pages; strengthened main theorem, proved undecidability in the language of rings without parameters