Algebra & Number Theory

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 . 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.

Article information

Source
Algebra Number Theory, Volume 7, Number 6 (2013), 1451-1479.

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

Permanent link to this document
https://projecteuclid.org/euclid.ant/1513730034

Digital Object Identifier
doi:10.2140/ant.2013.7.1451

Mathematical Reviews number (MathSciNet)
MR3107569

Zentralblatt MATH identifier
1343.11043

Subjects
Primary: 11D45: Counting solutions of Diophantine equations
Secondary: 14G05: Rational points

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

Citation

Frei, Christopher. Counting rational points over number fields on a singular cubic surface. Algebra Number Theory 7 (2013), no. 6, 1451--1479. doi:10.2140/ant.2013.7.1451. https://projecteuclid.org/euclid.ant/1513730034


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