  Let A be a Q-linear pseudo-abelian rigid tensor category. A notion of
finiteness due to Kimura and (independently) O'Sullivan guarantees that the
ideal of numerically trivial endomorphism of an object is nilpotent. We
generalize this result to special Schur-finite objects. In particular, in the
category of Chow motives, if X is a smooth projective variety which satisfies
the homological sign conjecture, then Kimura-finiteness, a special
Schur-finiteness, and the nilpotency of CH^{ni}(X^i\times X^i)_{num} for all i
(where n=dim X) are all equivalent.
