Courbes de Fermat et principe de Hasse
Let p≥3 be a prime number. A Fermat curve over Q of exponent p is defined by an equation of the form axp+byp+czp=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.
Authors
- Alain Kraus (ORCID: https://orcid.org/0000-0001-8891-0807)
Institutions
- Centre National de la Recherche Scientifique (FR)
- Université Paris Cité (FR)
- Sorbonne Université (FR)
- Sorbonne Paris Cité (FR)
Publication Details
- Journal
- Acta Arithmetica
- Published
- 2025-11-17
- DOI
- https://doi.org/10.4064/aa250111-4-8
- Primary Topic
- History and Theory of Mathematics
- Type
- article
- Field-Weighted Citation Impact
- 0.00