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.Comment: 15 pages; misprints correcte
