an:06435246
Zbl 1382.14006
Hoyois, Marc
From algebraic cobordism to motivic cohomology
EN
J. Reine Angew. Math. 702, 173-226 (2015).
00343918
2015
j
14F43 14F42 55N22 55U35
Summary: 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 \(S\)
\[
\mathrm{MGL}/(a_1,a_2,\dots)[1/c] \simeq H\mathbb{Z}[1/c]
\]
where \(H\mathbb{Z}\) is the motivic cohomology spectrum, MGL is the algebraic cobordism spectrum, and the elements \(a_n\) are generators of the Lazard ring. We discuss several applications including the computation of the slices of \(\mathbb{Z}[1/c]\)-local Landweber (see the work of \textit{M. Spitzweck} [``Relations between slices and quotients of the algebraic cobordism spectrum'', Homology Homotopy Appl. 12, No. 2, 335--351 (2010; \url{doi:10.4310/HHA.2010.v12.n2.a11}); J. \(K\)-Theory 9, No. 1, 103--117 (2012; Zbl 1249.14008)] exact motivic spectra and the convergence of the associated slice spectral sequences.
Zbl 1249.14008