On the torsion locus of the Ceresa normal function

We prove that the positive-dimensional part of the torsion locus of the Ceresa normal function in \mathcal{M}_g is not Zariski dense when g\geq 3. Moreover, it has only finitely many components with generic Mumford-Tate group equal to \mathrm{GSp}_{2g}; these components are defined over \overline{\mathbb{Q}}, and their union is closed under... Show more