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Kontsevich’s noncommutative numerical motives

Published online by Cambridge University Press:  12 October 2012

Matilde Marcolli
Affiliation:
Department of Mathematics, California Institute of Technology, 253-37 Caltech, 1200 E. California Blvd., Pasadena, CA 91125, USA (email: matilde@caltech.edu)
Gonçalo Tabuada
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Departamento de Matemática e CMA, FCT-UNL, Quinta da Torre, 2829-516 Caparica, Portugal (email: tabuada@math.mit.edu)
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Abstract

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In this article we prove that Kontsevich’s category NCnum(k)F of noncommutative numerical motives is equivalent to the one constructed by the authors in [Marcolli and Tabuada, Noncommutative motives, numerical equivalence, and semisimplicity, Amer. J. Math., to appear, available at arXiv:1105.2950]. As a consequence, we conclude that NCnum(k)F is abelian semi-simple as conjectured by Kontsevich.

Type
Research Article
Copyright
Copyright © Foundation Compositio Mathematica 2012

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