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Counting Rational Points on Cubic Hypersurfaces

Part of: Arithmetic problems. Diophantine geometry Arithmetic algebraic geometry

Published online by Cambridge University Press:  21 December 2009

T. D. Browning
T. D. Browning
Affiliation:
School of Mathematics, University of Bristol, Bristol, BS8 1TW. E-mail: t.d.browning@bristol.ac.uk
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Abstract

Let X ⊂ ℙN be a geometrically integral cubic hypersurface defined over ℚ, with singular locus of dimension at most dim X − 4. The main result in this paper is a proof of the fact that X(ℚ) contains OɛX (BdimX + ɛ) points of height at most B.

MSC classification

Secondary: 11G35: Varieties over global fields 14G05: Rational points
Type
Research Article
Information
Mathematika , Volume 54 , Issue 1-2 , December 2007 , pp. 93 - 112
Copyright
Copyright © University College London 2007

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References

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