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arXiv · 2112.00520

Experiments with Ceresa classes of cyclic Fermat quotients

David T. -B. G. Lilienfeldt·Ari Shnidman
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Abstract

We give two new examples of non-hyperelliptic curves whose Ceresa cycles have torsion images in the intermediate Jacobian. For one of them, the central value of the $L$-function of the relevant motive is non-vanishing and the Ceresa cycle is torsion in the Griffiths group, consistent with the conjectures of Beilinson and Bloch. We speculate on a possible explanation for the existence of these torsion Ceresa classes, based on some computations with cyclic Fermat quotients.

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David T. -B. G. Lilienfeldt, Ari Shnidman. 2021-12-01. Experiments with Ceresa classes of cyclic Fermat quotients. https://doi.org/10.1090/proc/16178

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