A motivic slice filtration for finite groups
The slice filtration by Voevodsky is a powerful and useful tool for understanding motivic spectra. A few years ago, joint with Paul Arne Ostvaer, we defined a filtration on $C_2$-equivariant motivic spectra, using an ad-hoc definition which mixed Voevodsky's slice filtration and Hill-Hopkins-Ravenel's filtration on equivariant spectra. I'll talk about recent(ish) developments in equivariant motivic homotopy which allow us to generalize this definition to a filtration for equivariant motivic spectra for finite (linearly reductive) groups and to compute the zero slice of the sphere (in characteristic zero).

