James Rawson

Ceresa Cycles of Modular Curves

For any curve there is a naturally attached algebraic cycle in its Jacobian, its Ceresa cycle. For a very general curve of genus at least 3 this is non-torsion, but explicitly determining whether it is torsion for any given example remains difficult. In this talk, I will discuss joint work with E. Lupoian, where we show that the Ceresa cycle is non-torsion for modular curves X_0(N) (of high enough level) by using it to construct rational points of infinite order on the Jacobian. As an application, we test a conjecture of Gross and Kudla connecting the height of the Ceresa cycle to triple product L functions.