Open Access
2013 Counting rational points over number fields on a singular cubic surface
Christopher Frei
Algebra Number Theory 7(6): 1451-1479 (2013). DOI: 10.2140/ant.2013.7.1451


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 . 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 x03=x1x2x3.


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Christopher Frei. "Counting rational points over number fields on a singular cubic surface." Algebra Number Theory 7 (6) 1451 - 1479, 2013.


Received: 10 April 2012; Revised: 30 July 2012; Accepted: 7 September 2012; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 1343.11043
MathSciNet: MR3107569
Digital Object Identifier: 10.2140/ant.2013.7.1451

Primary: 11D45
Secondary: 14G05

Keywords: Manin's conjecture , number fields , rational points , singular cubic surface

Rights: Copyright © 2013 Mathematical Sciences Publishers

Vol.7 • No. 6 • 2013
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