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Rational points of bounded height and the Weil restriction

Abstract

Given an extension of number fields EF and a projective variety X over F, we compare the problem of counting the number of rational points of bounded height on X with that of its Weil restriction over E. In particular, we consider the compatibility with respect to the Weil restriction of conjectural asymptotic formulae due to Manin and others. Using our methods we prove several new cases of these conjectures. We also construct new counterexamples over every number field.

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Correspondence to Daniel Loughran.

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Loughran, D. Rational points of bounded height and the Weil restriction. Isr. J. Math. 210, 47–79 (2015). https://doi.org/10.1007/s11856-015-1245-x

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  • DOI: https://doi.org/10.1007/s11856-015-1245-x

Keywords

  • Line Bundle
  • Rational Point
  • Toric Variety
  • Height Function
  • Pezzo Surface