Counting rational points over number fields on a singular cubic surface
Number Theory
2013-11-05 v2 Algebraic Geometry
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.
Cite
@article{arxiv.1204.0383,
title = {Counting rational points over number fields on a singular cubic surface},
author = {Christopher Frei},
journal= {arXiv preprint arXiv:1204.0383},
year = {2013}
}
Comments
22 pages, 1 figure; minor revision