Non-vanishing of Ceresa and Gross--Kudla--Schoen cycles associated to modular curves

Given an algebraic curve X of genus \ge 3, one can construct two algebraic 1-cycles, the Ceresa cycle and the Gross-Kudla-Schoen modified diagonal cycle, each living in the Jacobian of X and the triple product X \times X \times X respectively. These two cycles are homologically trivial but are of... Show more