Weak Approximation for Cubic Hypersurfaces of Large Dimension
Number Theory
2011-11-18 v1
Abstract
We address the problem of weak approximation for general cubic hypersurfaces defined over number fields, with arbitrary singular locus. In particular, weak approximation is established for the smooth locus of projective, geometrically integral, non-conical cubic hypersurfaces, of dimension at least 17. The proof utilises the Hardy-Littlewood circle method, and the fibration method.
Keywords
Cite
@article{arxiv.1111.4082,
title = {Weak Approximation for Cubic Hypersurfaces of Large Dimension},
author = {Mike Swarbrick Jones},
journal= {arXiv preprint arXiv:1111.4082},
year = {2011}
}