Homology of linear groups via cycles in $BG\times X$
| dc.creator | Knudson, Kevin P. | |
| dc.creator | Walker, Mark E. | |
| dc.date | 2003-11-20 | |
| dc.date.accessioned | 2026-07-07T05:03:06Z | |
| dc.date.available | 2026-07-07T05:03:06Z | |
| dc.description | 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 $G(\mathbb R)$. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/math/0311362 | |
| dc.identifier | http://arxiv.org/abs/math/0311362 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69279 | |
| dc.subject | K-Theory and Homology | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Algebraic Topology | |
| dc.subject | 14F42; 14C25; 19E15; 20G10; 55N91 | |
| dc.title | Homology of linear groups via cycles in $BG\times X$ | |
| dc.type | text |