Comptes Rendus
Number Theory/Dynamical Systems
Zhang's conjecture and squares of Abelian surfaces
Comptes Rendus. Mathématique, Volume 348 (2010) no. 9-10, pp. 483-486.

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.

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.

Received:
Accepted:
Published online:
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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