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arXiv · 1010.3922

Schur finiteness and nilpotency

Alessio Del Padrone·Carlo Mazza
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Abstract

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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Alessio Del Padrone, Carlo Mazza. 2010-10-19. Schur finiteness and nilpotency. https://doi.org/10.1016/j.crma.2005.07.010

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