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

TL;DR

This paper introduces a new filtration on the Chow group of zero-cycles for products of an abelian variety and curves, describing its structure via Somekawa K-groups, extending previous results.

Contribution

It defines a filtration on the Chow group for such products and explicitly describes the successive quotients using Somekawa K-groups, generalizing prior work.

Findings

Explicit generators and relations for the filtration quotients.

Description of the filtration's successive quotients via Somekawa K-groups.

Extension of previous results to more general product varieties.

Abstract

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.