English

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 Q\mathbb{Q} is Diophantine in Q(z)\mathbb{Q}(z). We provide a positive answer conditional on two standard conjectures on elliptic surfaces.

Keywords

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}
}