Rational Points on Diagonal Cubic Surfaces
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2014
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866915551139332096 |
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| author | Sato, Kazuki |
| author_facet | Sato, Kazuki |
| contents | We show under the assumption that the Tate-Shafarevich group of any elliptic curve over the rational numbers is finite that the cubic surface $x_1^3 + p_1p_2x_2^3 + p_2p_3x_3^3 + p_3p_1x_4^3 = 0$ has a rational point, where $p_1, p_2$ and $p_3$ are rational primes congruent to $2$ or $5$ modulo $9$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1409_8423 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | Rational Points on Diagonal Cubic Surfaces Sato, Kazuki Number Theory We show under the assumption that the Tate-Shafarevich group of any elliptic curve over the rational numbers is finite that the cubic surface $x_1^3 + p_1p_2x_2^3 + p_2p_3x_3^3 + p_3p_1x_4^3 = 0$ has a rational point, where $p_1, p_2$ and $p_3$ are rational primes congruent to $2$ or $5$ modulo $9$. |
| title | Rational Points on Diagonal Cubic Surfaces |
| topic | Number Theory |
| url | https://arxiv.org/abs/1409.8423 |