Comptes Rendus
no. 9-10
Number Theory/Dynamical Systems
Zhang's conjecture and squares of Abelian surfaces
[Conjecture de Zhang et carrés de surfaces abéliennes]

Présenté par : Christophe Soulé

Fabien Pazuki1
1 IMB U. Bordeaux 1, 351, cours de la Libération, 33405 Talence, France
Comptes Rendus. Mathématique, Volume 348 (2010) no. 9-10, pp. 483-486.

On donne dans cette Note des exemples de carrés de surfaces abéliennes violant la conclusion de la conjecture de Zhang sur l'intersection des sous-variétés et des points prépériodiques.

We give in this Note some squares of Abelian surfaces that are counterexamples to a conjecture formulated by Zhang about the intersection of subvarieties and preperiodic points.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.03.014
Fabien Pazuki 1

1 IMB U. Bordeaux 1, 351, cours de la Libération, 33405 Talence, France 
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Fabien Pazuki. Zhang's conjecture and squares of Abelian surfaces. Comptes Rendus. Mathématique, Volume 348 (2010) no. 9-10, pp. 483-486. doi : 10.1016/j.crma.2010.03.014. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.03.014/

[1] D. Ghioca, T. Tucker, S.-W. Zhang, Towards new dynamical conjectures, 2010, in preparation

[2] M. Hindry; J.H. Silverman Diophantine Geometry, GTM, vol. 201, Springer-Verlag, 2000

[3] J.H. Silverman Advanced Topics in the Arithmetic of Elliptic Curves, GTM, vol. 151, Springer-Verlag, 1994

[4] X. Yuan, S.-W. Zhang, Calabi theorem and algebraic dynamics, preprint

[5] S.-W. Zhang Distributions in Algebraic Dynamics, Survey in Differential Geometry, vol. 10, International Press, 2006, pp. 381-430

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