A remark on nilpotent correspondences, by Vladimir Guletskii

[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.

Vladimir Guletskii <alggeom@guletskii.org>