Algebraic Geometry Seminar
Tuesday, March 16, 2004, 4:00pm, 120 Physics
Kevin Knudson (Mississippi State University)
Homology of linear groups via cycles in BG x X

Abstract:

Let G be a linear algebraic group over a field k and let X be a nice scheme over k. I will construct a homology theory from cycles in the simplicial scheme BG x X in a style similar to the construction of motivic cohomology by Suslin--Voevodsky. When X is the spectrum of an algebraically closed field K, then the homology groups obtained are precisely the homology groups of the discrete group of K-rational points of G. Connections to Friedlander's Generalized Isomorphism Conjecture (which predicts the homology of G(K)) will be discussed, as will some interesting examples. Moreover, there is a connection between this theory and equivariant homology. This is joint work with Mark Walker.

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