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It is shown that the Grayson tower for
-theory of smooth algebraic varieties is isomorphic to the slice tower of
-spectra. We also extend the Grayson tower to bispectra, and show that the Grayson motivic spectral sequence is isomorphic to the motivic spectral sequence produced by the Voevodsky slice tower for the motivic
. This solves Suslin’s problem about these two spectral sequences in the affirmative.
For any perfect field k a triangulated category of K-motives is constructed in the style of Voevodsky's construction of the category . To each smooth k-variety X the K-motive is associated in the category and
where pt = Spec(k) and K(X) is Quillen's K-theory of X.
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