Vol. 7, No. 6, 2013

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ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Counting rational points over number fields on a singular cubic surface

Christopher Frei

Vol. 7 (2013), No. 6, 1451–1479
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.

Keywords
Manin's conjecture, number fields, rational points, singular cubic surface
Mathematical Subject Classification 2010
Primary: 11D45
Secondary: 14G05
Milestones
Received: 10 April 2012
Revised: 30 July 2012
Accepted: 7 September 2012
Published: 19 September 2013
Authors
Christopher Frei
Mathematisches Institut
LMU München
Theresienstr. 39
D-80333 München
Germany
http://www.mathematik.uni-muenchen.de/~frei