Tom Bachmann: Cohomology of Eilenberg–MacLane spaces

Abstract

Two decades ago Voevodsky determined the motivic Steenrod algebra: all bistable operations in motivic cohomology are generated by the motivic Steenrod operations that he constructed. He also remarked at the time that these operations do not generate the motivic cohomology of motivic Eilenberg–MacLane spaces. I will explain joint work in progress with Mike Hopkins where we determine these cohomologies. In particular we find the missing operations — somewhat surprisingly they just come from topology, no motives involved. Time permitting I will also talk about the motivic homology of free normed spectra, and the relationship between these two topics.