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Approximation diophantienne et distribution locale sur une surface torique

Volume 189 / 2019

Zhizhong Huang Acta Arithmetica 189 (2019), 1-94 MSC: Primary 11G50, 11K60, 14M25. DOI: 10.4064/aa170327-4-1 Published online: 26 April 2019

Abstract

We study Diophantine approximation and local distribution of rational points on a toric surface obtained as a blow-up of $\mathbb{P}^1\times\mathbb{P}^1$. It turns out that outside a Zariski closed subset the best approximations are achieved through a family of nodal curves. Hence the investigation is reduced to the question of local distribution of quadratic points on the projective line.

Authors

  • Zhizhong HuangInstitut Fourier, UMR 5582
    Université Grenoble Alpes
    38610 Gières, France
    and
    Institut für Algebra, Zahlentheorie und Diskrete Mathematik
    Leibniz Universität Hannover
    30167 Hannover, Allemagne
    e-mail

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