Counting rational points over number fields on a singular cubic surface

Christopher Frei

Type: Paratext

Publication Date: 2013-01-01

Citations: 0

DOI: https://doi.org/10.2140/ant.2013.7-6

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.

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Algebra & Number Theory - View - PDF
arXiv (Cornell University) - View - PDF
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+	Manin's conjecture for toric varieties	1995	Victor V. Batyrev Yuri Tschinkel
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+ PDF Chat	Manin's Conjecture for a Cubic Surface with D5 Singularity	2009	T. D. Browning Ulrich Derenthal
+ PDF Chat	On Manin's conjecture for a certain singular cubic surface	2007	R DELABRETECHE T. D. Browning Ulrich Derenthal
+ PDF Chat	The density of rational points on the cubic surface X 3 0= X 1 X 2 X 3	1999	D. R. Heath‐Brown B. Z. Moroz
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