Rational points of bounded height and the Weil restriction

Daniel Loughran

Rational points of bounded height and the Weil restriction

Number Theory 2015-02-17 v3 Algebraic Geometry

Authors: Daniel Loughran

Abstract

Given an extension of number fields $E \subset F$ 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.

Keywords

rational points bounded height Weil restriction number fields projective variety Manin conjecture asymptotic formulae

Cite

@article{arxiv.1210.1792,
  title  = {Rational points of bounded height and the Weil restriction},
  author = {Daniel Loughran},
  journal= {arXiv preprint arXiv:1210.1792},
  year   = {2015}
}

Comments

20 pages. Updated version includes proofs of new cases of Manin's conjecture. Some typos have also been corrected

Rational points of bounded height and the Weil restriction

Abstract

Keywords

Cite

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