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arXiv · 1210.7182

From algebraic cobordism to motivic cohomology

Marc Hoyois
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Abstract

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.

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Marc Hoyois. 2014-08-28. From algebraic cobordism to motivic cohomology. https://doi.org/10.1515/crelle-2013-0038

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