Diophantine stability for curves over finite fields

Brikena Vruoni; Francesc Bars; Joan Carles Lario

Diophantine stability for curves over finite fields

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arxiv 2409.07086 v2 pith:SWI6PJ3B submitted 2024-09-11 math.NT

Francesc Bars , Joan Carles Lario , Brikena Vruoni This is my paper

classification math.NT

keywords curvesdiophantinefieldsfinitestablealteredanalyzecarry

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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
math.AG 2025-06 conditional novelty 6.0 of 10

Curves over finite fields attain the Hallouin-Perret quadratic-extension bound exactly when all real parts of their Frobenius eigenvalues coincide, which yields new coefficient bounds and low-genus classifications.

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