English

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}
}
R2 v1 2026-06-28T18:40:50.706Z