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arXiv · 2404.11873

Non-torsion algebraic cycles on the Jacobians of Fermat quotients

Yusuke Nemoto
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Abstract

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.

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Yusuke Nemoto. 2024-04-18. Non-torsion algebraic cycles on the Jacobians of Fermat quotients. https://doi.org/10.4153/s0008439524000663

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