Holmstrom Motivic cobordism

Motivic cobordism

AG (Algebraic geometry)

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Motivic cobordism

Mixed

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Motivic cobordism

See Algebraic cobordism

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Motivic cobordism

arXiv:1210.7182 From algebraic cobordism to motivic cohomology fra arXiv Front: math.AG av Marc Hoyois 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.

arXiv:1206.5952 The motivic cobordism for group actions from arXiv Front: math.AG by Amalendu Krishna For a linear algebraic group $G$ over a field $k$, we define an equivariant version of the Voevodsky’s motivic cobordism $MGL$. We show that this is an oriented cohomology theory with localization sequence on the category of smooth $G$-schemes and there is a natural transformation from this functor to the functor of equivariant motivic cohomology. We give several applications. In particular, we use this equivariant motivic cobordism to study the cobordism ring of the classifying spaces and the cycle class maps from the algebraic to the singular cohomology of such spaces. This theory of motivic cobordism allows us to define the theory of motivic cobordism on the category of all smooth quotient stacks.

nLab page on Motivic cobordism