The slice filtration and mixed Tate motives, by Annette Huber and Bruno Kahn

[The original version, submitted Feb 3, 2005, has been slightly revised Oct 14, 2005.]

In this paper we study the "slice filtration" defined by effectivity conditions on Voevodsky's triangulated motives, and apply it to obtain spectral sequences converging to their 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. We apply this in particular to get spectral sequences converging to the motivic cohomology of a split connected reductive group.

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