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.
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Fabien Pazuki 1
@article{CRMATH_2010__348_9-10_483_0, author = {Fabien Pazuki}, title = {Zhang's conjecture and squares of {Abelian} surfaces}, journal = {Comptes Rendus. Math\'ematique}, pages = {483--486}, publisher = {Elsevier}, volume = {348}, number = {9-10}, year = {2010}, doi = {10.1016/j.crma.2010.03.014}, language = {en}, }
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
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[4] X. Yuan, S.-W. Zhang, Calabi theorem and algebraic dynamics, preprint
[5] Distributions in Algebraic Dynamics, Survey in Differential Geometry, vol. 10, International Press, 2006, pp. 381-430
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