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

Geometric and Functional Analysis volume 25, pages 671–732 (2015)Cite this article

Abstract

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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Authors and Affiliations

  1. School of Mathematics, University of Bristol, Bristol, BS8 1TW, UK

    T. D. Browning

  2. Department of Mathematics, University of York, York, YO10 5DD, UK

    P. Vishe

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  1. T. D. Browning
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  2. P. Vishe
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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). https://doi.org/10.1007/s00039-015-0328-5

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  • DOI: https://doi.org/10.1007/s00039-015-0328-5

Mathematics Subject Classification

  • 11G35 (11P55, 11T55, 14G05)