Weight structure on Kontsevich's noncommutative mixed motives
In this article we endow Kontsevich's triangulated category KMM[subscript 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-th...
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| Format: | Article |
| Language: | English |
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International Press of Boston, Inc.,
2013-09-24T18:41:32Z.
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| Online Access: | Get fulltext |
| Summary: | In this article we endow Kontsevich's triangulated category KMM[subscript 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[subscript 0](KMM[subscript 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. NEC Corporation Fund for Research in Computers and Communications (Award-2742738) |
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