A Diophantine definition of the constants in $\mathbb{Q}(z)$

Natalia Garcia-Fritz; Hector Pasten

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arXiv · 2208.11616

A Diophantine definition of the constants in $\mathbb{Q}(z)$

Natalia Garcia-Fritz·Hector Pasten

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Abstract

It is an old problem in the area of Diophantine definability to determine whether $\mathbb{Q}$ is Diophantine in $\mathbb{Q}(z)$. We provide a positive answer conditional on two standard conjectures on elliptic surfaces.

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Natalia Garcia-Fritz, Hector Pasten. 2022-08-24. A Diophantine definition of the constants in $\mathbb{Q}(z)$. https://arxiv.org/abs/2208.11616

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