English

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.

Keywords

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

R2 v1 2026-06-21T11:06:45.966Z