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Vanishing results in Chow groups for the modified diagonal cycles

Congling Qiu and Wei Zhang

Vol. 6 (2024), No. 2, 225–247
Abstract

We prove a sufficient condition for the vanishing of the modified diagonal cycle in the Chow group (with -coefficients) of the triple product of a curve over . We exhibit infinitely many nonhyperelliptic curves, including the Fricke–Macbeath curve, Bring’s curve, and two 1-dimensional families parameterized by certain Hurwitz spaces, for which our condition is satisfied.

Keywords
modified diagonal, Chow group, representation, Hurwitz curves, Fricke–Macbeath curve, Bring's curve
Mathematical Subject Classification
Primary: 11G30, 14C25
Milestones
Received: 7 May 2023
Revised: 28 November 2023
Accepted: 14 December 2023
Published: 29 June 2024
Authors
Congling Qiu
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA
United States
Wei Zhang
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA
United States