Abstract
We study a filtration of the algebraic K -theory spectrum of a smooth variety whose "layers" ought to give the motivic cohomology groups. The central result is a computation of the weight one layer of the filtration. The computations show that the homotopy groups of the weight one piece coincide with the weight one motivic cohomology groups, thus providing evidence that the filtration is correct. Additionally, a novel filtration of K 0 ( X ) is studied, where X is any quasi-projective variety.
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