Rational points on quartic hypersurfaces

T. D. Browning; D. R. Heath-Brown

doi:10.1515/CRELLE.2009.026

Published by De Gruyter February 24, 2009

Rational points on quartic hypersurfaces

T. D. Browning and D. R. Heath-Brown

From the journal Journal für die reine und angewandte Mathematik

https://doi.org/10.1515/CRELLE.2009.026

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Abstract

Let X be a projective non-singular quartic hypersurface of dimension 39 or more, which is defined over ℚ. We show that X(ℚ) is non-empty provided that X(ℝ) is non-empty and X has p-adic points for every prime p.

Received: 2007-06-07

Revised: 2008-01-08

Published Online: 2009-02-24

Published in Print: 2009-April

Rational points on quartic hypersurfaces

Abstract

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