[Nov 4, 2004: The author has requested the paper be removed, because
of a gap in the proof of the main result.]
[September 26, 2004: An updated version has been provided: the author
corrected a mistake appeared in the previous version.]
[an updated version has been provided, Jan 27, 2004: added a few
explanations to the proof of the main result and improved the second
part of the preprint]
[an updated version has been provided, Sep 3, 2003]
In this note we show that, if the motive of a nonsingular projective
variety is Schur-finite, then any numerically trivial correspondence
on it is nilpotent. This yields an exact geometrical interpretation
of Schur finiteness for motives, introduced recently by C. Mazza, and
provides a motivic localization of Bloch's conjecture for surfaces of
general type without globally holomorphic 2-forms.