A Diophantine definition of the constants in $\mathbb{Q}(z)$
Number Theory
2022-09-20 v2 Logic
Abstract
It is an old problem in the area of Diophantine definability to determine whether is Diophantine in . We provide a positive answer conditional on two standard conjectures on elliptic surfaces.
Cite
@article{arxiv.2208.11616,
title = {A Diophantine definition of the constants in $\mathbb{Q}(z)$},
author = {Natalia Garcia-Fritz and Hector Pasten},
journal= {arXiv preprint arXiv:2208.11616},
year = {2022}
}