The optimality of the Bounded Height Conjecture
Journal de Théorie des Nombres de Bordeaux, Volume 21 (2009) no. 3, pp. 771-786.

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.

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

Received:
Revised:
Published online:
DOI: 10.5802/jtnb.702
Classification: 11G50,  14H52,  14K12
Keywords: Height, Elliptic curves, Subvarieties
Evelina Viada 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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Evelina Viada. The optimality of the Bounded Height Conjecture. Journal de Théorie des Nombres de Bordeaux, Volume 21 (2009) no. 3, pp. 771-786. doi : 10.5802/jtnb.702. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.702/

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