Powers of abelian varieties over $\overline{\mathbb Q(t)}$ not isogenous to a Jacobian
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915635372490752 |
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| author | Fortman, Olivier de Gaay Shankar, Ananth N. |
| author_facet | Fortman, Olivier de Gaay Shankar, Ananth N. |
| contents | We prove the existence of abelian varieties over $\overline{\mathbb Q(t)}$ with no power isogenous to a Jacobian. Moreover, given a positive integer $N$, we prove the existence of abelian varieties over $\overline{\mathbb Q(t)}$ with maximal monodromy such that the $n$th power is not isogenous to a Jacobian for $n \leq N$. We make use of an Arakelov inequality established by Lu and Zuo, as well as intersection theoretic methods, to prove our main results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19410 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Powers of abelian varieties over $\overline{\mathbb Q(t)}$ not isogenous to a Jacobian Fortman, Olivier de Gaay Shankar, Ananth N. Algebraic Geometry Number Theory We prove the existence of abelian varieties over $\overline{\mathbb Q(t)}$ with no power isogenous to a Jacobian. Moreover, given a positive integer $N$, we prove the existence of abelian varieties over $\overline{\mathbb Q(t)}$ with maximal monodromy such that the $n$th power is not isogenous to a Jacobian for $n \leq N$. We make use of an Arakelov inequality established by Lu and Zuo, as well as intersection theoretic methods, to prove our main results. |
| title | Powers of abelian varieties over $\overline{\mathbb Q(t)}$ not isogenous to a Jacobian |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2511.19410 |