Diophantine stability for curves over finite fields
Number Theory
2025-05-14 v2
Abstract
We carry out a survey on curves defined over finite fields that are Diophantine stable; that is, with the property that the set of points of the curve is not altered under a proper field extension. First, we derive some general results of such curves and then we analyze several families of curves that happen to be Diophantine stable.
Keywords
Cite
@article{arxiv.2409.07086,
title = {Diophantine stability for curves over finite fields},
author = {Francesc Bars and Joan Carles Lario and Brikena Vruoni},
journal= {arXiv preprint arXiv:2409.07086},
year = {2025}
}