Schur finiteness and nilpotency
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...
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Veröffentlicht in: | arXiv.org 2010-10 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | 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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ISSN: | 2331-8422 |
DOI: | 10.48550/arxiv.1010.3922 |