Abstract
We show that the ambiguity of Murre's Chow-Kuenneth projector for degree 1 has certain good properties, assuming only that it factors through a Chow motive of a smooth irreducible curve. This is compatible with a picture obtained by using Beilinson's conjectural mixed motives, and implies for instance the independence of the Chow motive defined by the middle Chow-Kuenneth projector for surfaces.
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