Rational points of bounded height and the Weil restriction

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  • Daniel Loughran
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Details

Original languageEnglish
Pages (from-to)47-79
Number of pages33
JournalIsrael journal of mathematics
Volume210
Issue number1
Publication statusPublished - 1 Sept 2015

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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Rational points of bounded height and the Weil restriction. / Loughran, Daniel.
In: Israel journal of mathematics, Vol. 210, No. 1, 01.09.2015, p. 47-79.

Research output: Contribution to journalArticleResearchpeer review

Loughran D. Rational points of bounded height and the Weil restriction. Israel journal of mathematics. 2015 Sept 1;210(1):47-79. doi: 10.1007/s11856-015-1245-x
Loughran, Daniel. / Rational points of bounded height and the Weil restriction. In: Israel journal of mathematics. 2015 ; Vol. 210, No. 1. pp. 47-79.
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