We provide a sfficient condition that ensures the nilpotency of endomorphisms universally of trace zero of Schur-finite objects in a category of homological type, i.e., a Q-linear-category with a tensor functor to super vector spaces. We present some applications in the category of motives, where out result generalizes previous results about finite-dimensional objects, in particular by Kimura. We also present some facts which suggest that this mightbe the best generalization possible of this line of proof.
Schur-finite motives and trace identities / D.P. A., C. Mazza - In: 18th Congress of Unione Matematica Italiana / [a cura di] F. Altomare. - [s.l] : Unione Matematica Italiana, 2009. - ISBN 978-88-96336-02-1. - pp. 401-408 (( Intervento presentato al 18. convegno Congresso dell'Unione Matematica Italiana tenutosi a Bari nel 2007.
Schur-finite motives and trace identities
C. MazzaUltimo
2009
Abstract
We provide a sfficient condition that ensures the nilpotency of endomorphisms universally of trace zero of Schur-finite objects in a category of homological type, i.e., a Q-linear-category with a tensor functor to super vector spaces. We present some applications in the category of motives, where out result generalizes previous results about finite-dimensional objects, in particular by Kimura. We also present some facts which suggest that this mightbe the best generalization possible of this line of proof.
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