Weak Approximation for Cubic Hypersurfaces of Large Dimension

2011/11/17 by Mike Swarbrick Jones, Jones, Mike Swarbrick
Mathematics · #11D72 #11G35 (Primary) 11D25 #11P55 #14G25 (Secondary) #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11D25 #msc:11D72 #msc:11G35 #msc:11P55 #msc:14G25

paper · pdf · doi:10.48550/arxiv.1111.4082

arxiv created 2011/11/17 · arxiv updated 2011/11/18

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.

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