Relations between slices and quotients of the algebraic cobordism spectrum

Abstract

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.

15 pages; misprints corrected

References in corpus (4)

• On the zero slice of the sphere spectrum
• Chern classes, K-theory and Landweber exactness over nonregular base schemes
• Comparison of cobordism theories
• Slices of motivic Landweber spectra