Weak approximation for cubic hypersurfaces of large dimension. (English) Zbl 1368.11058

Summary: 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, nonconical cubic hypersurfaces of dimension at least 17. The proof utilises the Hardy-Littlewood circle method and the fibration method.


11G35 Varieties over global fields
11D25 Cubic and quartic Diophantine equations
11D72 Diophantine equations in many variables
11P55 Applications of the Hardy-Littlewood method
14G25 Global ground fields in algebraic geometry
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