Rational points on cubic hypersurfaces that split off a form
Number Theory
2019-02-20 v1 Algebraic Geometry
Abstract
Let X be a projective cubic hypersurface of dimension 11 or more, which is defined over the rationals. In this paper it is shown that X contains rational points provided that the cubic form defining X can be written as the sum of two forms that share no common variables. ----- This paper features an appendix "Groupe de Brauer non ramifi\'e des hypersurfaces cubiques singuli\`eres (d'apr\`es P. Salberger)", by J.-L. Colliot-Th\'l\`ene.
Cite
@article{arxiv.0808.0125,
title = {Rational points on cubic hypersurfaces that split off a form},
author = {T. D. Browning},
journal= {arXiv preprint arXiv:0808.0125},
year = {2019}
}
Comments
34 pages; appendix by J.-L. Colliot-Th\'el\`ene