WEIGHT TWO MOTIVIC COHOMOLOGY OF CLASSIFYING SPACES FOR SEMISIMPLE GROUPS

Let f : X -> Y be a torsor for a semisimple group G with Y a smooth and geometrically irreducible variety over an arbitrary field. We relate the etale motivic cohomology of weight two for X, Y and G. We also compute the ' etale motivic cohomology groups of degree at most 4 for the classifying space of G. This result was used in an another work by the author for the computation of the group of degree 3 cohomological invariants of semisimple groups with coefficients in Q/Z(2).