On torsion sections of elliptic fibrations
数论
2007-05-23 v1 代数几何
摘要
Let E be an elliptic curve over the function field Q(t). Suppose that for every number field L\not=Q and every element tau\in L such that the specialization E_tau is smooth, the curve E_tau has a non-trivial torsion point over L. We show that E has a non-trivial torsion point over Q(t). This provides evidence in support of a question of Graber-Harris-Mazur-Starr on rational pseudo-sections of arithmetic surjective morphisms.
引用
@article{arxiv.math/0509168,
title = {On torsion sections of elliptic fibrations},
author = {Siman Wong},
journal= {arXiv preprint arXiv:math/0509168},
year = {2007}
}