We consider Murre’s conjectures on Chow groups for a fourfold which is a product of two curves and a surface. We give a result which concerns Conjecture D:the kernel of a certain projector is equal to the homologically trivial part of the Chow group. We also give a proof of Conjecture B for a product of two surfaces.
J. Math. Kyoto Univ.
47(3):
621-629
(2007).
DOI: 10.1215/kjm/1250281027