ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 14, 19, 55: q Soulé, Christophe, CNRS, IHES, France Filtrations on Higher Algebraic K-theory 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_{γ}^{p} of these groups. There exist also the filtration coming from the Brown-Gersten spectral sequence (the algebraic analog of the Atiyah-Hirzebruch spectral sequence) and, in the case of a variety X over a field, the filtration F_{codim}^{p} by codimension of supports. We compare these filtrations and we get in particular the inclusion

F_{γ}^{p}K_{m}(X) ∈ F_{codim}^{p−m}K_{m}(X).

This is joint work with H. Gillet. Reference: H. Gillet and C. Soulé, Filtrations on Higher Algebraic K-theory, preprint (1984, revised in 1998).