Chow motives versus non-commutative motives
By Gonçalo Tabuada. 2011
58 citations recorded by the source corpus.
In this article we formalize and enhance Kontsevich's beautiful insight that Chow motives can be embedded into non-commutative ones after factoring out by the action of the Tate object. We illustrate the potential of this result by developing three of its manyfold applications: (1) the notions of Schur and Kimura finiteness admit an adequate extension to the realm of non-commutative motives; (2) Gillet-Soule's motivic measure admits an extension to the Grothendieck ring of non-commutative motives; (3) certain motivic zeta functions admit an intrinsic construction inside the category of non-commutative motives.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/97a3b246e1b8fdf4f72234049d2fcb38f12115f0
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In Algebra and Number Theory
In Discrete Mathematics and Combinatorics
In Geometry and Topology
Citations in the corpus
- Norms in motivic homotopy theory (2017, background): “ mapping space Map( 1rA; !1rB) in Chow nc(R) is the K-theory space K(A RB!;op). Thus, the homotopy category h 1Chow nc(R) is the opposite of Kontsevich’s category of noncommutative Chow motives over R[Tab13]. If p: R!R0is nite etale, the norm p : Catcg R0 !Cat cg R preserves smooth and proper 1-cate”