An infinitesimal approach to the study of cycles on abelian varieties

Abstract

This paper is a work in progress on Bloch’s conjecture asserting the vanishing of the Pontryagin product of a [Formula: see text] codimensional cycle on an abelian variety by [Formula: see text] zero cycles of degree zero. We prove an infinitesimal version of the conjecture and we discuss in particular, the case of [Formula: see text]-dimensional cycles.