Approximation diophantienne et distribution locale sur une surface torique

Abstract

In this article we study Diophantine approximation and local distribution of a rational point 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 a quadratic point on the projective line.

in French. Miscellaneous corrections and improvements. To appear in Acta Arithmetica. Comments are welcome!

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• Rational approximations on toric varieties
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