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Published November 2012 | Submitted
Journal Article Open

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.

Additional Information

© 2012 Foundation Compositio Mathematica. Received 27 September 2011, accepted in final form 27 April 2012, published online 12 October 2012. The first author was partially supported by the NSF grants DMS-0901221, DMS-1007207 and DMS-1201512. The second author was partially supported by the NEC award 2742738 and by the Portuguese Foundation for Science and Technology through PEst-OE/MAT/UI0297/2011 (CMA). The authors are very grateful to Yuri Manin for stimulating discussions and to the anonymous referees for their comments, corrections and questions, which have greatly improved the article.

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August 19, 2023
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