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.
Accepté le :
Publié le :
@article{CRMATH_2010__348_9-10_483_0, author = {Pazuki, Fabien}, 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}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2010.03.014/} }
TY - JOUR AU - Pazuki, Fabien TI - Zhang's conjecture and squares of Abelian surfaces JO - Comptes Rendus. Mathématique PY - 2010 SP - 483 EP - 486 VL - 348 IS - 9-10 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2010.03.014/ DO - 10.1016/j.crma.2010.03.014 LA - en ID - CRMATH_2010__348_9-10_483_0 ER -
%0 Journal Article %A Pazuki, Fabien %T Zhang's conjecture and squares of Abelian surfaces %J Comptes Rendus. Mathématique %D 2010 %P 483-486 %V 348 %N 9-10 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2010.03.014/ %R 10.1016/j.crma.2010.03.014 %G en %F CRMATH_2010__348_9-10_483_0
Pazuki, Fabien. Zhang's conjecture and squares of Abelian surfaces. Comptes Rendus. Mathématique, Tome 348 (2010) no. 9-10, pp. 483-486. doi : 10.1016/j.crma.2010.03.014. http://archive.numdam.org/articles/10.1016/j.crma.2010.03.014/
[1] D. Ghioca, T. Tucker, S.-W. Zhang, Towards new dynamical conjectures, 2010, in preparation
[2] Diophantine Geometry, GTM, vol. 201, Springer-Verlag, 2000
[3] 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] Distributions in Algebraic Dynamics, Survey in Differential Geometry, vol. 10, International Press, 2006, pp. 381-430
Cité par Sources :