The optimality of the Bounded Height Conjecture
Viada, Evelina1
1 Université de Fribourg Suisse, Pérolles Département de Mathématiques Chemin du Musée 23 CH-1700 Fribourg, Switzerland Supported by the SNF (Swiss National Science Foundation)
Journal de théorie des nombres de Bordeaux, Tome 21 (2009) no. 3, pp. 771-786.

Nous démontrons que la “conjecture de hauteur bornée” est optimale dans le sens suivant. Soit V une variété irréductible dans une puissance d’une courbe elliptique. Si les sous-variétés anormales de V recouvrent tout V, alors chaque ouvert de V a une hauteur non bornée. Nous donnons aussi quelques exemples

In this article we show that the Bounded Height Conjecture is optimal in the sense that, if V is an irreducible subvariety with empty deprived set in a power of an elliptic curve, then every open subset of V does not have bounded height. The Bounded Height Conjecture is known to hold. We also present some examples and remarks.

DOI : 10.5802/jtnb.702
Classification : 11G50, 14H52, 14K12
Mots-clés : Height, Elliptic curves, Subvarieties
Viada, Evelina 1

1 Université de Fribourg Suisse, Pérolles Département de Mathématiques Chemin du Musée 23 CH-1700 Fribourg, Switzerland Supported by the SNF (Swiss National Science Foundation) 
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Viada, Evelina. The optimality of the Bounded Height Conjecture. Journal de théorie des nombres de Bordeaux, Tome 21 (2009) no. 3, pp. 771-786. doi : 10.5802/jtnb.702. http://www.numdam.org/articles/10.5802/jtnb.702/

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