From algebraic cobordism to motivic cohomology

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Abstract Let S be an essentially smooth scheme over a field of characteristic exponent c. We prove that there is a canonical equivalence of motivic spectra over S MGL/(a 1,a 2,...)[1/c] ≃ Hℤ[1/c] where Hℤ is the motivic cohomology spectrum, MGL is the algebraic cobordism spectrum, and the elements an are generators of the Lazard ring. We discuss several applications including the computation of the slices of ℤ[1/c]-local Landweber exact motivic spectra and the convergence of the associated slice spectral sequences.