Elvira Lupoian

The Ceresa cycle is an algebraic cycle attached to a smooth algebraic curve with a marked point, which is always homologically trivial. Ceresa proved that for a very general complex curve of genus at least 3, this cycle is not trivial as an element in the Griffiths group.  Notably, hyperelliptic curves with a Weierstrass point have trivial Ceresa cycle. Beyond this, there are few explicit examples where triviality/non-triviality is known. In this talk I will discuss the non-vanishing of the Ceresa cycle attached to the modular curve X_0(N). This is joint work with James Rawson.