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Journal of the Ramanujan Mathematical Society

Volume 34, Issue 3, September 2019  pp. 271–279.

Sufficient conditions for the existence of rational points on diagonal cubic surfaces

Authors:  Yosuke Shimizu
Author institution:Bannnai laboratory at Keio University in Japan

Summary:  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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