Courbes de Fermat et principe de Hasse

2025/05/13 by Kraus, Alain
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2505.08363

Abstract

Let p≥ 3 be a prime number. A Fermat curve over ℚ of exponent p is defined by an equation of the shape ax^p+by^p+cz^p=0, where a,b,c are non-zero rational numbers. We prove in this article that there exist infinitely many Fermat curves defined over ℚ, of exponent p, pairwise non ℚ-isomorphic, contradicting the Hasse principle.

Citations

• Contre-exemples au principe de Hasse pour les courbes de Fermat

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