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The hypothetical existence of a good theory of mixed motives predicts manydeep phenomena related to algebraic cycles. One of these, a generalization ofBloch's conjecture says that "small Hodge diamonds" go with "small Chowgroups". Voisin's method (which produces examples with small Chow groups) isanalyzed carefully to widen its applicability. A threefold of general typewithout 1- and 2-forms is exhibited for which this extension yields Bloch'sgeneralized conjecture.

BLOCH-TYPE CONJECTURES AND AN EXAMPLE A THREE-FOLD OF GENERAL TYPE