Kontsevich™s noncommutative numerical motives

Abstract

In this article we prove that Kontsevich™s category NC num(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 NC num(k) F is abelian semi-simple as conjectured by Kontsevich. © 2012 Foundation Compositio Mathematica.