Algebraic points of bounded height on the projective line

Points algébriques de hauteur bornée sur la droite projective

Cécile Le Rudulier (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We consider an absolute adelic height on the set of algebraic points of the projective line P-1, associate to an ample line bundle. We give an asymptotic formula for the number of algebraic points of fixed degree and of height lower than B, when B tends to infinity. The case of the standard height on P-1 has been studied by Masser and Vaaler. We generalize this result for any adelic height using a geometric point of view and one of he known cases of the Batyrev-Manin conjecture.

Mots clés: Varieties; Theorem

Domaines: Géométrie algébrique [math.AG]

Cécile Le Rudulier. Algebraic points of bounded height on the projective line. Journal de Théorie des Nombres de Bordeaux, 2014, 26 (3), pp.789-812. ⟨10.5802/jtnb.888⟩. ⟨hal-01143234⟩