arXiv subjects

Mike Swarbrick Jones

Publications and source records attributed to Mike Swarbrick Jones.

2 recordsLinked to original sources

arXiv2011

Weak Approximation for Cubic Hypersurfaces of Large Dimension

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.

math.NT↗

arXiv2011

A Note On a Theorem of Heath-Brown and Skorobogatov

We generalise a result of Heath-Brown and Skorobogatov to show that a certain class of varieties over a number field $k$ satisfies Weak Approximation and the Hasse Principle, provided there is no Brauer-Manin obstruction.

math.NT↗