Courbes de Fermat et principe de Hasse
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909608725970944 |
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| author | Kraus, Alain |
| author_facet | Kraus, Alain |
| contents | Let $p\geq 3$ be a prime number. A Fermat curve over $\mathbb{Q}$ 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 $\mathbb{Q}$, of exponent $p$, pairwise non $\mathbb{Q}$-isomorphic, contradicting the Hasse principle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_08363 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Courbes de Fermat et principe de Hasse Kraus, Alain Number Theory Let $p\geq 3$ be a prime number. A Fermat curve over $\mathbb{Q}$ 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 $\mathbb{Q}$, of exponent $p$, pairwise non $\mathbb{Q}$-isomorphic, contradicting the Hasse principle. |
| title | Courbes de Fermat et principe de Hasse |
| topic | Number Theory |
| url | https://arxiv.org/abs/2505.08363 |