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Rational points of bounded height and the Weil restriction

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Abstract

Given an extension of number fields E ⊂ F 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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Authors and Affiliations

  1. Institut für Algebra, Zahlentheorie und Diskrete Mathematik, Leibniz Universität Hannover, Welfengarten 1, 30167, Hannover, Germany

    Daniel Loughran

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  1. Daniel Loughran
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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

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