Counting rational points over number fields on a singular cubic surface

Details Counting rational points over number fields on a singular cubic surface Counting rational points over number fields on a singular cubic surface

2012-04-02

arxiv.org/abs/1204.0383v1

Mathematics

Number Theory

22 pages, 1 figure

Scientific paper

A conjecture of Manin predicts the distribution of K-rational points on certain algebraic varieties defined over a number field K. In recent years, a method using universal torsors has been successfully applied to several hard special cases of Manin's conjecture over the field Q of rational numbers. Combining this method with techniques developed by Schanuel, we give a proof of Manin's conjecture over arbitrary number fields for the singular cubic surface S given by the equation w^3 = x y z.

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