Remarks on Murre's conjecture on Chow groups
  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 $X\times C.$ 
Kejian Xu, Ze Xu
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