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APPLICATION OF MOTIVIC COMPLEXES TO NEGLIGIBLE CLASSES

Lichtenbaum's complex enables one to relate Galois cohomology to K ­cohomo­ logy groups. In this paper, we consider the first terms of the Hochschild­Serre spectral sequence for the cohomology of these complexes, which was developed by Kahn, in the case of quotients of "big" open sets in cellular varieties. In the particular case of a faithful representation W of a finite group G over an algebraically closed field k, this yields that the group of negligible classes in the cohomology group H 3 (G,Q/Z(2)) is canonically isomorphic to the second equivariant Chow group of a point. It also implies that the unramified classes in the cohomology group H 3 (k(W) G ,(Q/Z) ' (2)) come from the cohomology of G, which had been proved by Saltman when k is the field of complex numbers. Using the motivic complexes of Voevodsky, we then prove similar results in degrees four and five.