Algebra & Number Theory
- Algebra Number Theory
- Volume 7, Number 6 (2013), 1451-1479.
Counting rational points over number fields on a singular cubic surface
A conjecture of Manin predicts the distribution of -rational points on certain algebraic varieties defined over a number field . 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 given by the equation .
Algebra Number Theory, Volume 7, Number 6 (2013), 1451-1479.
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
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 11D45: Counting solutions of Diophantine equations
Secondary: 14G05: Rational points
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