Abstract:

I will report on work in progress, joint with Aravind Asok and Mike Hopkins,
in which we establish a motivic analog of the classical Freudenthal suspension
theorem. That is, for a pointed motivic space X over a field of characteristic
zero, which is n-connected "in both the S^1- and Gm-direction", we show that
the natural map X -> Omega^{2,1}Sigma^{2,1}X is roughly 2n-conected (again in
both S^1- and Gm-direction).