In this article we show that the Bounded Height Conjecture is optimal in the sense that, if is an irreducible subvariety with empty deprived set in a power of an elliptic curve, then every open subset of 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 une variété irréductible dans une puissance d’une courbe elliptique. Si les sous-variétés anormales de recouvrent tout , alors chaque ouvert de a une hauteur non bornée. Nous donnons aussi quelques exemples
Revised:
Published online:
DOI: 10.5802/jtnb.702
Classification: 11G50, 14H52, 14K12
Keywords: Height, Elliptic curves, Subvarieties
Author's affiliations:
@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 = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.702/} }
TY - JOUR TI - The optimality of the Bounded Height Conjecture JO - Journal de Théorie des Nombres de Bordeaux PY - 2009 DA - 2009/// SP - 771 EP - 786 VL - 21 IS - 3 PB - Université Bordeaux 1 UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.702/ UR - https://zbmath.org/?q=an%3A1203.11048 UR - https://www.ams.org/mathscinet-getitem?mr=2605547 UR - https://doi.org/10.5802/jtnb.702 DO - 10.5802/jtnb.702 LA - en ID - JTNB_2009__21_3_771_0 ER -
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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