Schur finiteness and nilpotency

Details Schur finiteness and nilpotency Schur finiteness and nilpotency

2010-10-19

arxiv.org/abs/1010.3922v1

Comptes Rendus Math. 341 (2005) 283-286

Mathematics

Algebraic Geometry

Scientific paper

10.1016/j.crma.2005.07.010

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.

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