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Rational points on cubic hypersurfaces over \({\mathbb{F}_{q}(t)}\)


The Hasse principle and weak approximation is established for non-singular cubic hypersurfaces X over the function field \({\mathbb{F}_q(t)}\), provided that char \({(\mathbb{F}_{q})>{3}}\) and X has dimension at least 6.

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Browning, T.D., Vishe, P. Rational points on cubic hypersurfaces over \({\mathbb{F}_{q}(t)}\) . Geom. Funct. Anal. 25, 671–732 (2015).

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Mathematics Subject Classification

  • 11G35 (11P55, 11T55, 14G05)