A Filtration of the Chow Group of Zero-Cycles for a Product of Curves and an Abelian Variety

In this paper we define a descending filtration on the Chow group of zero cycles for varieties of the form $A\times C_1\times \cdots \times C_d$ where $A$ is an abelian variety and each $C_i$ is a smooth projective curve. We give explicit generators and relations for the successive quotients of this filtration by showing that they can be described by Somekawa K-groups. This extends the work of Raskind and Spiess who proved this result for products of curves and Gazaki who proved this for abelian varieties.