Geometry and Physics Seminar: Ben Williams

If X is a variety over a field, the Chow groups of X are defined in terms of closed subvarieties of X and form a kind of cohomology theory for X. Higher Chow groups, defined by Spencer Bloch in the 1980s in terms of subvarieties on X x A^m and now related to the theory of motivic cohomology, extend the theory of Chow groups, and may be nonzero even when the ordinary Chow groups vanish. I will explain how the higher Chow groups of GLn are related to a 'suspension' of the ordinary Chow groups of projective space. Time permitting, I will conjecture how this relationship might extend to 'suspensions' of the Chow groups of Grassmanians.