The optimality of the Bounded Height Conjecture
Journal de théorie des nombres de Bordeaux, Volume 21 (2009) no. 3, p. 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

DOI : https://doi.org/10.5802/jtnb.702
Classification:  11G50,  14H52,  14K12
Keywords: Height, Elliptic curves, Subvarieties
@article{JTNB_2009__21_3_771_0,
     author = {Viada, Evelina},
     title = {The optimality of the Bounded Height Conjecture},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux 1},
     volume = {21},
     number = {3},
     year = {2009},
     pages = {771-786},
     doi = {10.5802/jtnb.702},
     mrnumber = {2605547},
     zbl = {1203.11048},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_2009__21_3_771_0}
}
Viada, Evelina. 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. http://www.numdam.org/item/JTNB_2009__21_3_771_0/

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