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Kontsevich’s noncommutative numerical motives

Published:2012-10-12 Issue:6 Volume:148 Page:1811-1820
ISSN:0010-437X
Container-title:Compositio Mathematica
language:en
Short-container-title:Compositio Math.

Author:

Marcolli Matilde,Tabuada Gonçalo

Abstract

AbstractIn 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.

Publisher

Wiley

Subject

Algebra and Number Theory

Reference25 articles.

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3. [MT11a] Marcolli M. and Tabuada G. , Noncommutative motives, numerical equivalence, and semi-simplicity, Amer. J. Math., to appear, available at arXiv:1105.2950.

4. [Kon10] Kontsevich M. , Mixed noncommutative motives, Talk at the FRG Workshop on Homological Mirror Symmetry, University of Miami, 2010, notes available at www-math.mit.edu/auroux/frg/miami10-notes.

5. Notes on Motives in Finite Characteristic

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