Rational Points on Diagonal Cubic Surfaces

Kazuki Sato

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arXiv · 1409.8423

Rational Points on Diagonal Cubic Surfaces

Kazuki Sato

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Abstract

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 $9$.

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Kazuki Sato. 2014-09-30. Rational Points on Diagonal Cubic Surfaces. https://arxiv.org/abs/1409.8423

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