Elden Elmanto (Copenhagen): Power Operations on Normed Motivic Spectra

The genuine analog of an E_\infty-ring spectrum in algebraic geometry is the notion of a normed motivic spectrum, which carries multiplicative transfers along finite etale morphisms. The homological shadows of an E_\infty-ring structure are the Dyer-Lashof operations which acts on the homology an E_\infty-ring spectrum. We will construct analogs of these operations in motivic homotopy theory, state their basic properties and discuss some consequences such as splitting results for normed motivic spectra. The construction mixes two ingredients: the theory of motivic colimits and equivariant motivic homotopy theory. This is joint work with Tom Bachmann and Jeremiah Heller.