Experiments with Ceresa classes of cyclic Fermat quotients

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.

Accepted Manuscript, to appear in Proceedings of the American Mathematical Society

References in corpus (2)

• Multiplicative Chow-Künneth decompositions and varieties of cohomological K3 type
• Nontrivial algebraic cycles in the Jacobian varieties of some quotients of Fermat curves

Cited by in corpus (4)

• Group-theoretic Johnson classes and a non-hyperelliptic curve with torsion Ceresa class
• Vanishing results in Chow groups for the modified diagonal cycles
• Vanishing criteria for Ceresa cycles
• Non-torsion algebraic cycles on the Jacobians of Fermat quotients