Non-torsion algebraic cycles on the Jacobians of Fermat quotients
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910834911870976 |
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| author | Nemoto, Yusuke |
| author_facet | Nemoto, Yusuke |
| contents | We study the Abel-Jacobi image of the Ceresa cycle $W_{k, e}-W_{k, e}^-$, where $W_{k, e}$ is the image of the $k$th symmetric product of a curve $X$ with a base point $e$ on its Jacobian variety. For certain Fermat quotient curves of genus $g$, we prove that for any choice of the base point and $k \leq g-2$, the Abel-Jacobi image of the Ceresa cycle is non-torsion. In particular, these cycles are non-torsion modulo rational equivalence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_11873 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-torsion algebraic cycles on the Jacobians of Fermat quotients Nemoto, Yusuke Algebraic Geometry 14C25, 14F35, 14H40 We study the Abel-Jacobi image of the Ceresa cycle $W_{k, e}-W_{k, e}^-$, where $W_{k, e}$ is the image of the $k$th symmetric product of a curve $X$ with a base point $e$ on its Jacobian variety. For certain Fermat quotient curves of genus $g$, we prove that for any choice of the base point and $k \leq g-2$, the Abel-Jacobi image of the Ceresa cycle is non-torsion. In particular, these cycles are non-torsion modulo rational equivalence. |
| title | Non-torsion algebraic cycles on the Jacobians of Fermat quotients |
| topic | Algebraic Geometry 14C25, 14F35, 14H40 |
| url | https://arxiv.org/abs/2404.11873 |