Fix a rational basepoint b and a rational number c. For the quadratic dynamical system , it has been shown that the number of rational points in the backward orbit of b is bounded independent of the choice of rational parameter c. In this short Note we investigate the dependence of the bound on the basepoint b, assuming a strong form of the Mordell Conjecture.
Soit b un point cible rationnel, et soit c un nombre rationnel. Pour le système dynamique quadratique , il a été montré que le nombre de points rationnels dans l'orbite inverse de b est borné indépendamment du choix du paramètre rationnel c. Dans cette courte Note, nous étudions la dépendance en le point cible b, en supposant une forme forte de la Conjecture de Mordell.
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X.W.C. Faber 1
@article{CRMATH_2010__348_7-8_355_0, author = {X.W.C. Faber}, title = {A remark on the effective {Mordell} {Conjecture} and rational pre-images under quadratic dynamical systems}, journal = {Comptes Rendus. Math\'ematique}, pages = {355--358}, publisher = {Elsevier}, volume = {348}, number = {7-8}, year = {2010}, doi = {10.1016/j.crma.2010.02.010}, language = {en}, }
TY - JOUR AU - X.W.C. Faber TI - A remark on the effective Mordell Conjecture and rational pre-images under quadratic dynamical systems JO - Comptes Rendus. Mathématique PY - 2010 SP - 355 EP - 358 VL - 348 IS - 7-8 PB - Elsevier DO - 10.1016/j.crma.2010.02.010 LA - en ID - CRMATH_2010__348_7-8_355_0 ER -
X.W.C. Faber. A remark on the effective Mordell Conjecture and rational pre-images under quadratic dynamical systems. Comptes Rendus. Mathématique, Volume 348 (2010) no. 7-8, pp. 355-358. doi : 10.1016/j.crma.2010.02.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.02.010/
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