On the torsion locus of the Ceresa normal function
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912092525690880 |
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| author | Kerr, Matt Tayou, Salim |
| author_facet | Kerr, Matt Tayou, Salim |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19366 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the torsion locus of the Ceresa normal function Kerr, Matt Tayou, Salim Algebraic Geometry Number Theory 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. |
| title | On the torsion locus of the Ceresa normal function |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2406.19366 |