Filtrations on Higher Algebraic K-theory, by Henri Gillet and Christophe Soulé

Using the theory of simplicial sheaves one can define a lambda-ring structure on higher K-groups of simplicial schemes hence a gamma-filtration F^p_gamma of these groups. There exist also the filtration coming from the Brown-Gersten spectral sequence and, in the case of a variety X over a field, the filtration F^p_codim by codimension of supports. We compare these filtrations and we get in particular the inclusion F^p_gamma K_m(X) in F^{p-m}_codim K_m(X).

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