有限域上曲线的 Diophantine 稳定性

arXiv - MATH - Number Theory Pub Date : 2024-09-11 DOI:arxiv-2409.07086

Francesc Bars, Joan Carles Lario

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引用次数: 0

摘要

我们对定义在有限域上的狄奥凡汀稳定曲线进行了研究，即曲线的点集在适当的域扩展下不会改变。首先，我们推导出这类曲线的一些一般结果，然后分析了恰好是 Diophantine 稳定曲线的几个曲线族。

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Diophantine stability for curves over finite fields

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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arXiv - MATH - Number Theory

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