Homology, Homotopy and Applications
Volume 14 (2012)
Weight structure on Kontsevich’s noncommutative mixed motives
Pages: 129 – 142
In this article we endow Kontsevich’s triangulated category $KMM_k$ of noncommutative mixed motives with a non-degenerate weight structure in the sense of Bondarko. As an application we obtain: (1) a convergent weight spectral sequence for every additive invariant (e.g., algebraic $K$-theory, cyclic homology, topological Hochschild homology, etc.); (2) a ring isomorphism between $K_0(KMM_k)$ and the Grothendieck ring of the category of noncommutative Chow motives; (3) a precise relationship between Voevodsky’s (virtual) mixed motives and Kontsevich’s noncommutative (virtual) mixed motives.
weight structure, weight spectral sequence, Grothendieck ring, Picard group, Voevodsky motive, Kontsevich noncommutative motive
2010 Mathematics Subject Classification
14A22, 18D20, 18G40, 19L10