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arXiv · 2409.07086

Diophantine stability for curves over finite fields

Francesc Bars·Joan Carles Lario·Brikena Vruoni
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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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Francesc Bars, Joan Carles Lario, Brikena Vruoni. 2024-09-11. Diophantine stability for curves over finite fields. https://arxiv.org/abs/2409.07086

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