Comptes Rendus
Algebra/Algebraic Geometry
Schur finiteness and nilpotency
Comptes Rendus. Mathématique, Volume 341 (2005) no. 5, pp. 283-286.

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 CHni(Xi×Xi)num for all i (where n=dimX) are all equivalent.

Soit A une catégorie tensorielle rigide pseudo-abélienne Q-lineaire. Une notion de finitude de Kimura et (indépendamment) O'Sullivan garantit que l'idéal des endomorphismes numériquement triviaux d'un objet est nilpotent. Nous généralisons ce résultat à certains objets Schur-finis. En particulier, dans la catégorie des motifs de Chow, si X est une variété projective lisse purement de dimension n qui satisfait la conjecture homologique de signe, alors la finitude de Kimura, l'annulation du motif de X par un certain foncteur de Schur, et la nilpotence de CHni(Xi×Xi)num pour tous i, sont équivalentes.

Published online:
DOI: 10.1016/j.crma.2005.07.010

Alessio Del Padrone 1; Carlo Mazza 2

1 Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, 16146 Genova, Italy
2 Institute for Advanced Study, 1, Einstein Drive, 08854 Princeton, NJ, USA
     author = {Alessio Del Padrone and Carlo Mazza},
     title = {Schur finiteness and nilpotency},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {283--286},
     publisher = {Elsevier},
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     number = {5},
     year = {2005},
     doi = {10.1016/j.crma.2005.07.010},
     language = {en},
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%A Carlo Mazza
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Alessio Del Padrone; Carlo Mazza. Schur finiteness and nilpotency. Comptes Rendus. Mathématique, Volume 341 (2005) no. 5, pp. 283-286. doi : 10.1016/j.crma.2005.07.010.

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