We prove a relative statement about the slices of the algebraic cobordism spectrum. If the map from MGL to a certain quotient of MGL introduced by Hopkins and Morel is the map to the zero-slice then a relative version of Voevodsky's conjecture on the slices of MGL holds true. We outline the picture for K-theory and rational slices.
Homology, Homotopy and Applications, Vol. 12 (2010), No. 2, pp.335-351.
Available as: dvi dvi.gz ps ps.gz pdf