The optimality of the Bounded Height Conjecture
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.

Reçu le : 2007-12-20
Révisé le : 2008-12-18
Publié le : 2010-03-22
DOI : https://doi.org/10.5802/jtnb.702
Classification : 11G50,  14H52,  14K12
Mots clés : Height, Elliptic curves, Subvarieties
@article{JTNB_2009__21_3_771_0,
     author = {Evelina Viada},
     title = {The optimality of the Bounded Height Conjecture},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {771--786},
     publisher = {Universit\'e Bordeaux 1},
     volume = {21},
     number = {3},
     year = {2009},
     doi = {10.5802/jtnb.702},
     zbl = {1203.11048},
     mrnumber = {2605547},
     language = {en},
     url = {jtnb.centre-mersenne.org/item/JTNB_2009__21_3_771_0/}
}
Evelina Viada. 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. https://jtnb.centre-mersenne.org/item/JTNB_2009__21_3_771_0/

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