On the torsion locus of the Ceresa normal function

Matt Kerr; Salim Tayou

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arXiv · 2406.19366

On the torsion locus of the Ceresa normal function

Matt Kerr·Salim Tayou

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Abstract

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 the action of $\mathrm{Gal}(\overline{\mathbb{Q}}/\mathbb Q)$. More generally, we study the distribution of the torsion locus of arbitrary admissible normal functions.

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Matt Kerr, Salim Tayou. 2024-06-27. On the torsion locus of the Ceresa normal function. https://arxiv.org/abs/2406.19366

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