Hilbert's Tenth Problem over Function Fields of Positive Characteristic Not Containing the Algebraic Closure of a Finite Field
Number Theory
2013-06-13 v1 Logic
Abstract
We prove that the existential theory of any function field of characteristic is undecidable in the language of rings provided that the constant field does not contain the algebraic closure of a finite field. We also extend the undecidability proof for function fields of higher transcendence degree to characteristic 2 and show that the first-order theory of {\bf any} function field of positive characteristic is undecidable in the language of rings without parameters.
Keywords
Cite
@article{arxiv.1306.2669,
title = {Hilbert's Tenth Problem over Function Fields of Positive Characteristic Not Containing the Algebraic Closure of a Finite Field},
author = {Kirsten Eisentraeger and Alexandra Shlapentokh},
journal= {arXiv preprint arXiv:1306.2669},
year = {2013}
}