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The slice filtration and mixed Tate motives

Published online by Cambridge University Press:  14 July 2006

Annette Huber  and
Bruno Kahn
Annette Huber
Affiliation:
Mathematisches Institut, Augustusplatz 10/11, 04109 Leipzig, Germanyhuber@mathematik.uni-leipzig.de
Bruno Kahn
Affiliation:
Institut de Mathématiques de Jussieu, 175–179 rue du Chevaleret, 75013 Paris, Francekahn@math.jussieu.fr
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Abstract

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Using the ‘slice filtration’, defined by effectivity conditions on Voevodsky's triangulated motives, we define spectral sequences converging to their motivic cohomology and étale motivic cohomology. These spectral sequences are particularly interesting in the case of mixed Tate motives as their $E_2$-terms then have a simple description. In particular this yields spectral sequences converging to the motivic cohomology of a split connected reductive group. We also describe in detail the multiplicative structure of the motive of a split torus.

Keywords

motivesbirational motivesslice filtrationTate motivestoric fibrationsreductive groups14F22 (primary)14F2014C2520G15
Type
Research Article
Information
Compositio Mathematica , Volume 142 , Issue 4 , July 2006 , pp. 907 - 936
Copyright
Foundation Compositio Mathematica 2006