Sequences of rational torsions on abelian varieties
The author gives some families of special curves of higher genus, which contain a rational torsion divisor whose order depends linearly or quadratically on the genus. Moreover, by using the jacobian varieties of these special curves, he notes that there exists a series of abelian varieties over \(\mathbb{Q}\) with a rapidly increasing sequence of torsions. For the elliptic curves over \(\mathbb{Q}\), \textit{B. Mazur} [in Modular Funct. one Variable, V. Proc. internat. Conf., Bonn 1976, Lect. Notes Math. 601, 107-148 (1977; Zbl 0357.14005)] decides the rational torsions on them.
scientific article; zbMATH DE number 59807