## 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.

Translated title of the contribution | Rational points on quartic hypersurfaces |
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Original language | English |

Journal | Journal für die reine und angewandte Mathematik |

Volume | Submitted |

Publication status | Accepted/In press - 2007 |