Geodesic
Schur-Finite Motives and Trace Identities
Bollettino della Unione matematica italiana, Série 9, Tome 2 (2009) no. 1, pp. 37-44.

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We provide a sufficient condition that ensures the nilpotency of endomorphisms universally of trace zero of Schur-finite objects in a category of homological type, i.e., a $\mathbb{Q}$-linear $\otimes$-category with a tensor functor to super vector spaces. We present some applications in the category of motives, where our result generalizes previous results about finite-dimensional objects, in particular by Kimura. We also present some facts which suggest that this might be the best generalization possible of this line of proof. 
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Del Padrone, Alessio; Mazza, Carlo. Schur-Finite Motives and Trace Identities. Bollettino della Unione matematica italiana, Série 9, Tome 2 (2009) no. 1, pp. 37-44. http://geodesic.mathdoc.fr/item/BUMI_2009_9_2_1_a1/

[AK02] Yves André - Bruno Kahn, Nilpotence, radicaux et structures monoïdales, Rend. Sem. Mat. Univ. Padova, 108 (2002), 107-291. | fulltext EuDML | MR

[And04] Yves André, Une introduction aux motifs (motifs purs, motifs mixtes, périodes), Panoramas et Synthèses [Panoramas and Syntheses], 17, Société Mathématique de France (Paris, 2004). | MR | Zbl

[Ber88] Allan Berele, Trace identities and $\mathbb{Z}/2\mathbb{Z}$-graded invariants, Trans. Amer. Math. Soc., 309, no. 2 (1988), 581-589. | DOI | MR | Zbl

[Del02] Pierre Deligne, Catégories tensorielles, Mosc. Math. J., 2, no. 2 (2002), 227-248. | MR

[DP06] Alessio Del Padrone, Schur functors, nilpotency and motives, Phd thesis, Università degli Studi di Genova, Dipartimento di Matematica, 2006 (2006).

[DPM] Alessio Del Padrone - Carlo Mazza, Schur finiteness and nd endomorphisms universally of trace zero via certain trace relations, To appear in Comm. in Alg. | DOI | MR | Zbl

[DPM05] Alessio Del Padrone - Carlo Mazza, Schur finiteness and nilpotency, C. R. Math. Acad. Sci. Paris, 341, no. 5 (2005), 283-286. | DOI | MR

[FH91] William Fulton - Joe Harris, Representation theory, Graduate Texts in Mathematics, 129 (1991), xvi+551. | DOI | MR | Zbl

[GP03] Vladimir Guletskiǐ - Claudio Pedrini, Finite-dimensional motives and the conjectures of Beilinson and Murre, K-Theory, 30, no. 3 (2003), 243-263. | DOI | MR | Zbl

[Jan94] Uwe Jannsen, Motivic sheaves and filtrations on Chow groups, Motives (Seattle, WA, 1991), Proc. Sympos. Pure Math., 55, (1994), 245-302. | MR | Zbl

[Jan07] Uwe Jannsen, On finite-dimensional motives and Murre's conjecture, Algebraic Cycles and Motives, London Math. Soc. Lecture Note Ser., 344 (2007), 420-450. | MR | Zbl

[JSV96] André Joyal - Ross Street - Dominic Verity, Traced monoidal categories, Math. Proc. Cambridge Philos. Soc., 119, n0. 3 (1996), 447-468. | DOI | MR | Zbl

[Kah] Bruno Kahn, On the multiplicities of a motive, Preprint, February 5, 2007, K-theory Preprint Archives, http://www.math.uiuc.edu/K-theory/0818/.

[Kim05] Shun-Ichi Kimura, Chow groups are finite dimensional, in some sense, Math. Ann., 331, no. 1 (2005), 173-201. | DOI | MR | Zbl

[Maz04] Carlo Mazza, Schur functors and motives, K-Theory, 33, no. 2 (2004), 89-106. | DOI | MR

[Sai] Morihiko Saito, Bloch's Conjecture and Chow Motives, Preprint, February 7, 2000, arXiv, http://arxiv.org/abs/math/0002009v2.