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Chow motives versus non-commutative motives

By Goncalo Tabuada

Abstract

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.Comment: 12 page

Topics: Mathematics - K-Theory and Homology, Mathematics - Algebraic Geometry, Mathematics - Algebraic Topology
Year: 2011
OAI identifier: oai:arXiv.org:1103.0200
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