An infinitesimal approach to the study of Cycles on Abelian Varieties

This paper is a work in progress on Bloch’s conjecture asserting the vanishing of the Pontryagin product of a $p$ codimensional cycle on an abelian variety by $p+1$ zero cycles of degree zero. We prove an infinitesimal version of the conjecture and we discuss, in particular, the case of $3$ dimensional cycles.