设G是一个代数群，X是域k上的光滑整概形.本文通过考虑单纯形概型$BG\times X (an idea suggested by Andrei Suslin). We discuss the basic properties of these groups and construct a spectral sequence, beginning with the groups $ H_i（Δ^j，G）$, which converges to the etale cohomology of the simplicial group BG. These groups are therefore connected with the study of Friedlander's generalized isomorphism conjecture. <p> We also compute some examples, focusing in particular on the case X=Spec(k). In the case where k is the real numbers, there is a connection between the groups $ H_i $ and the Z/2-equivariant cohomology of the classifying space of the discrete group $ G（\mathbb R）$中的圈，构造了同调型群$H_i(X,G)$.
英文摘要：
Let G be an algebraic group and let X be a smooth integral scheme over a field k. In this paper we construct homology-type groups $H_i(X,G)$ by considering cycles in the simplicial scheme $BG\times X (an idea suggested by Andrei Suslin). We discuss the basic properties of these groups and construct a spectral sequence, beginning with the groups $H_i(Δ^j,G)$, which converges to the etale cohomology of the simplicial group BG. These groups are therefore connected with the study of Friedlander's generalized isomorphism conjecture. <p> We also compute some examples, focusing in particular on the case X=Spec(k). In the case where k is the real numbers, there is a connection between the groups $H_i$ and the Z/2-equivariant cohomology of the classifying space of the discrete group $G(\mathbb R)$.
