Summary: We show that there is an equivalence of categories between the orthogonal components for the slice filtration and the birational motivic stable homotopy categories which are constructed in this paper. Relying on this equivalence, we are able to describe the slices for projective spaces (including $\ P ^{\infty}$), Thom spaces and blow ups.

14F42

birational invariants, motivic homotopy theory, motivic spectral sequence, slice filtration