Counting rational points over number fields on a singular cubic surface

Christopher Frei

doi:10.2140/ant.2013.7-6

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arXiv · 1204.0383

Counting rational points over number fields on a singular cubic surface

Christopher Frei

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Abstract

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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BibTeX RIS

Christopher Frei. 2013-11-04. Counting rational points over number fields on a singular cubic surface. https://doi.org/10.2140/ant.2013.7-6

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