Diophantine stability for curves over finite fields

2024/09/11 by Bars, Francesc, Lario, Joan Carles, Vruoni, Brikena · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2409.07086

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.

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• Maximal Curves With Respect To Quadratic Extensions Over Finite Fields

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