English

Chow motives versus non-commutative motives

K-Theory and Homology 2011-03-02 v1 Algebraic Geometry Algebraic Topology

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.

Keywords

Cite

@article{arxiv.1103.0200,
  title  = {Chow motives versus non-commutative motives},
  author = {Goncalo Tabuada},
  journal= {arXiv preprint arXiv:1103.0200},
  year   = {2011}
}

Comments

12 pages

R2 v1 2026-06-21T17:33:39.647Z