Heights of Gross-Schoen and Ceresa Cycles

In this talk, we construct a Zariski open dense locus in Mg

on which the Beilinson-Bloch height of the Gross-Schoen and Ceresa cycles is a Weil height, i.e. it has a lower bound and satisfies the Northcott property. This implies a generic positivity result of the heights of these cycles. This is joint work with Shouwu Zhang.