Counting rational points over number fields on a singular cubic surface

@article{Frei2012CountingRP,
  title={Counting rational points over number fields on a singular cubic surface},
  author={Christopher Frei},
  journal={arXiv: Number Theory},
  year={2012}
}
  • C. Frei
  • Published 2 April 2012
  • Mathematics
  • arXiv: Number Theory
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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