Remarks on Murre's conjecture on Chow groups

TL;DR

This paper investigates Murre's conjecture on Chow groups for specific product varieties, proving it holds for certain fourfolds formed by a curve and either an elliptic modular threefold or an abelian threefold.

Contribution

It proves Murre's conjecture (B) for fourfolds formed by the product of a curve with either an elliptic modular threefold or an abelian threefold.

Findings

Murre's conjecture (B) holds for X×C where X is an elliptic modular threefold or an abelian threefold.

The result applies to fourfolds over an algebraically closed field of characteristic 0.

Provides evidence supporting Murre's conjecture for specific classes of product varieties.

Abstract

For certain product varieties, Murre's conjecture on Chow groups is investigated. In particular, it is proved that Murre's conjecture (B) is true for two kinds of four-folds. Precisely, if $C$ is a curve and $X$ is an elliptic modular threefold over $k$ (an algebraically closed field of characteristic 0) or an abelian variety of dimension 3, then Murre's conjecture (B) is true for the fourfold $X\times C.$