Weak Approximation for Cubic Hypersurfaces of Large Dimension

Details Weak Approximation for Cubic Hypersurfaces of Large Dimension Weak Approximation for Cubic Hypersurfaces of Large Dimension

2011-11-17

arxiv.org/abs/1111.4082v1

Mathematics

Number Theory

Scientific paper

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.

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