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On finite dimensionality of mixed Tate motives

Published online by Cambridge University Press:  04 September 2008

Shahram Biglari
Shahram Biglari
Affiliation:
Fakultät für Mathematik, Universität Bielefeld, D-33501 Bielefeld, Germany, [email protected].
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Abstract

We prove a few results concerning the notion of finite dimensionality of mixed Tate motives in the sense of Kimura and O'Sullivan. It is shown that being oddly or evenly finite dimensional is equivalent to vanishing of certain cohomology groups defined by means of the Levine weight filtration. We then explain the relation to the Grothendieck group of the triangulated category D of mixed Tate motives. This naturally gives rise to a λ–ring structure on K0(D).

Keywords

Tate motiveGrothendieck group
Type
Research Article
Information
Journal of K-Theory , Volume 4 , Issue 1 , August 2009 , pp. 145 - 161
Copyright
Copyright © ISOPP 2009

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