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Non-torsion algebraic cycles on the Jacobians of Fermat quotients

Part of: Cycles and subschemes (Co)homology theory Curves

Published online by Cambridge University Press:  22 November 2024

Yusuke Nemoto Open the ORCID record for Yusuke Nemoto [Opens in a new window]
Yusuke Nemoto*
Affiliation:
Department of Mathematics and Informatics, Graduate School of Science, Chiba University, Yayoicho 1-33, Inage, Chiba, 263-8522, Japan.
*
e-mail: y-nemoto@waseda.jp
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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.

Keywords

Abel-Jacobi mapCeresa cycleFermat quotient

MSC classification

Primary: 14C25: Algebraic cycles 14F35: Homotopy theory; fundamental groups 14H40: Jacobians, Prym varieties

Information

Type
Article
Information
Canadian Mathematical Bulletin , Volume 68 , Issue 1 , March 2025 , pp. 60 - 72
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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