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

• Autorzy: Alain Kraus
• Języki publikacji: FR EN

Abstrakty

EN

Let p be an odd prime number. In this paper, we are concerned with the behaviour of Fermat curves defined over ℚ, given by equations $ax^{p} + by^{p} + cz^{p} = 0$, with respect to the local-global Hasse principle. It is conjectured that there exist infinitely many Fermat curves of exponent p which are counterexamples to the Hasse principle. This is a consequence of the abc-conjecture if p ≥ 5. Using a cyclotomic approach due to H. Cohen and Chebotarev's density theorem, we obtain a partial result towards this conjecture, by proving it for p ≤ 19.

Kategorie tematyczne

• 11D41: Higher degree equations; Fermat's equation

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2016
• Tom: 174
• Numer: 2
• Strony: 189-197

Daty

wydano

2016

Twórcy

autor

Alain Kraus

• Université de Paris VI, Institut de Mathématiques de Jussieu, 4 Place Jussieu, 75005 Paris, France

Identyfikatory

DOI

10.4064/aa8420-4-2016