Journal of the Ramanujan Mathematical Society

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Sufficient Conditions for the Existence of Rational Points on Diagonal Cubic Surfaces


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1 Bannnai laboratory at Keio University in Japan, Japan
     

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In this paper, we construct diagonal cubic surfaces over ℚ which have a ℚ-rational point under the assumption that the Tate-Shafarevich group of elliptic curve X3 + Y3 = AZ3 is finite. We can also check that there is no Brauer-Manin obstruction for these surfaces without the finiteness assumption of the Tate-Shafarevich group.
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  • Sufficient Conditions for the Existence of Rational Points on Diagonal Cubic Surfaces

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Authors

Yosuke Shimizu
Bannnai laboratory at Keio University in Japan, Japan

Abstract


In this paper, we construct diagonal cubic surfaces over ℚ which have a ℚ-rational point under the assumption that the Tate-Shafarevich group of elliptic curve X3 + Y3 = AZ3 is finite. We can also check that there is no Brauer-Manin obstruction for these surfaces without the finiteness assumption of the Tate-Shafarevich group.

References