Online Talk

Classical Wilson spaces are topological spaces such that both the homotopy groups and the homology groups are free abelian groups concentrated in even degrees. The most famous (and, in some sense, all) examples are the even loop spaces of the complex cobordism spectrum MU. While the fact that these have even homotopy goes back to Quillen, the even homology is a somewhat more recent result due to Wilson. In fact the homology of these spaces admits a conceptual description, due to Ravenel and Wilson, as a certain universal "Hopf ring".

I will report on work establishing a motivic analog of this result: the motives of the motivic spaces comprising the algebraic cobordism spectrum MGL are split Tate ("even") and in fact are described by the same universal Hopf ring. Joint work with M. Hopkins