Geodesic
Non-torsion algebraic cycles on the Jacobians of Fermat quotients
Canadian mathematical bulletin, Tome 68 (2025) no. 1, pp. 60-72

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DOI

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.
DOI : 10.4153/S0008439524000663
Mots-clés : Abel-Jacobi map, Ceresa cycle, Fermat quotient 
Nemoto, Yusuke. Non-torsion algebraic cycles on the Jacobians of Fermat quotients. Canadian mathematical bulletin, Tome 68 (2025) no. 1, pp. 60-72. doi: 10.4153/S0008439524000663
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     title = {Non-torsion algebraic cycles on the {Jacobians} of {Fermat} quotients},
     journal = {Canadian mathematical bulletin},
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     year = {2025},
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