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Description

By work of Voevodsky, the slice filtration in motivic homotopy theory provides a powerful tool for computing homotopy groups of motivic spectra. In this talk, I will describe the motivic slice filtration and the effective slice spectral sequence it produces. Then I will discuss how the motivic effective slice spectral sequence gives rise to a spectral sequence in $C_2$ equivariant homotopy theory. One of the main applications is computing the homotopy groups of $ko_{C_2}$, the connective $C_2$ equivariant $K$ theory. This gives a reproof of work by Guillou-Hill-Isaksen-Ravenel that computes homotopy of $ko_{C_2}$ using equivariant Adams spectral sequence.