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We prove a relative statement about the slices of the algebraic cobordismspectrum. If the map from MGL to a certain quotient of MGL introduced byHopkins and Morel is the map to the zero-slice then a relative version ofVoevodsky's conjecture on the slices of MGL holds true. We outline the picturefor K-theory and rational slices.

Relations between slices and quotients of the algebraic cobordism spectrum