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Rational points on quartic hypersurfaces

T. D. Browning·D. R. Heath-Brown
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Abstract

Let X be a non-singular projective hypersurface of degree 4, which is defined over the rational numbers. Assume that X has dimension 39 or more, and that X contains a real point and p-adic points for every prime p. Then X is shown to contain infinitely many rational points.

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T. D. Browning, D. R. Heath-Brown. 2008-01-08. Rational points on quartic hypersurfaces. https://arxiv.org/abs/math/0701348

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