Weight structure on Kontsevich's noncommutative mixed motives

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Abstract

In this article we endow Kontsevich’s triangulated cate- gory KMMk 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 K0(KMMk) 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.
Original languageUnknown
Pages (from-to)129-142
JournalHomology, Homotopy and Applications
Volume14
Issue number2
DOIs
Publication statusPublished - 1 Jan 2012

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