Abstract

For a field of characteristic zero Levine has proved in [M. Levine, Mixed motives, Math. Surv. Monogr. 57, American Mathematical Society, 1998.], Part I, Ch. VI, 2.5.5, that the triangulated tensor categories of motives defined in [V. Voevodsky, Triangulated categories of motives over a field, Cycles, transfers, and motivic homology theories, Ann. Math. Stud. 143, Princeton University Press, Princeton, NJ, 2000.] and [M. Levine, Mixed motives, Math. Surv. Monogr. 57, American Mathematical Society, 1998.] are equivalent. Using some results of [F. Ivorra, Réalisation ℓ-adique des motifs triangulés géométriques I, Preprint K-theory/0762, January 2006.], in this paper we show that the strategy of Levine's proof can also be applied on every perfect field to the categories of triangulated motives with rational coefficients or to the pseudo-abelian hulls of the integral tensor subcategories generated by motives of smooth projective schemes.