Non-torsion algebraic cycles on the Jacobians of Fermat quotients

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.