A universality theorem for Voevodsky's algebraic cobordism spectrum

Ivan Panin, Konstantin Pimenov and Oliver Röndigs

An algebraic version of a theorem of Quillen is proved. More precisely, for a regular Noetherian scheme S of finite Krull dimension, we consider the motivic stable homotopy category SH(S) of Pro¹-spectra, equipped with the symmetric monoidal structure described in [7]. The algebraic cobordism Pro¹-spectrum MGL is considered as a commutative monoid equipped with a canonical orientation th^MGL ∈ MGL^2,1(Th(O(-1))). For a commutative monoid E in the category SH(S), it is proved that the assignment φ ↦ φ(th^MGL) identifies the set of monoid homomorphisms φ : MGL → E in the motivic stable homotopy category SH(S) with the set of all orientations of E. This result generalizes a result of G. Vezzosi in [12].

Homology, Homotopy and Applications, Vol. 10 (2008), No. 2, pp.211-226.

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