From algebraic cobordism to motivic cohomology

Marc Hoyois
2015 Journal für die Reine und Angewandte Mathematik  
Let S be an essentially smooth scheme over a field of characteristic exponent c. Let MGL and HZ denote the algebraic cobordism spectrum and the motivic cohomology spectrum over S, respectively. We show that the canonical map MGL/(a1, a2, ...) -> HZ induced by the additive orientation of motivic cohomology becomes an equivalence after inverting c. As an application, we prove the convergence of the Atiyah-Hirzebruch spectral sequence for all Z[1/c]-local Landweber exact motivic spectra.
doi:10.1515/crelle-2013-0038 fatcat:76xghnacgzgdlcvxzrlx4nuuuu