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Rational points on cubic hypersurfaces that split off a form. With an appendix by J.-L. Colliot-Thélène

Part of: Forms and linear algebraic groups Diophantine equations

Published online by Cambridge University Press:  15 February 2010

T. D. Browning
T. D. Browning*
Affiliation:
School of Mathematics, University of Bristol, Bristol BS8 1TW, UK (email: t.d.browning@bristol.ac.uk)
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Abstract

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Let X be a projective cubic hypersurface of dimension 11 or more, which is defined over ℚ. We show that X(ℚ) is non-empty provided that the cubic form defining X can be written as the sum of two forms that share no common variables.

Keywords

Hasse principlecubic hypersurfacesHardy–Littlewood circle method

MSC classification

Secondary: 11D72: Equations in many variables 11E76: Forms of degree higher than two
Type
Research Article
Information
Compositio Mathematica , Volume 146 , Issue 4 , July 2010 , pp. 853 - 885
Copyright
Copyright © Foundation Compositio Mathematica 2010

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