On the dimension of Voisin sets in the moduli space of abelian varieties

We study the subsets ()
abelian variety A consisting in the collection of points ∈
such that the zero-cycle {}−{0}
is k-nilpotent with respect to the Pontryagin product in the Chow group. These sets were introduced recently by Voisin
in the moduli space of abelian varieties of dimension g with a fixed polarization, where 2()
is positive dimensional. We estimate the dimension of Voisin sets