Abstract
Let k be a field with a real embedding. We compare the motivic slice filtration of a motivic spectrum over Spec(k) with the C-2-equivariant slice filtration of its equivariant Betti realization, giving conditions under which realization induces an equivalence between the associated slice towers. In particular, we show that, up to reindexing, the towers agree for all spectra obtained from ...
Abstract
Let k be a field with a real embedding. We compare the motivic slice filtration of a motivic spectrum over Spec(k) with the C-2-equivariant slice filtration of its equivariant Betti realization, giving conditions under which realization induces an equivalence between the associated slice towers. In particular, we show that, up to reindexing, the towers agree for all spectra obtained from localized quotients of MGL and MR, and for motivic Landweber exact spectra and their realizations. As a consequence, we deduce that equivariant spectra obtained from localized quotients of MR are even in the sense of Hill and Meier, and give a computation of the slice spectral sequence converging to pi*,*BP < n >/2 for 1 <= n <= infinity.
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