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arXiv · 2512.00569

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

Thomas Jaklitsch
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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.

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Thomas Jaklitsch. 2025-11-29. A Filtration of the Chow Group of Zero-Cycles for a Product of Curves and an Abelian Variety. https://arxiv.org/abs/2512.00569

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