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arXiv · 0709.4116

A universality theorem for Voevodsky's algebraic cobordism spectrum

I. Panin·K. Pimenov·O. Röndigs
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Abstract

An algebraic version of a theorem due to Quillen is proved. More precisely, for a ground field k we consider the motivic stable homotopy category SH(k) of P^1-spectra equipped with the symmetric monoidal structure described in arXiv:0709.3905v1 [math.AG]. The algebraic cobordism P^1-spectrum MGL is considered as a commutative monoid equipped with a canonical orientation. For a commutative monoid E in the category SH(k) we identify the set of monoid homomorphisms from MGL to E in the motivic stable homotopy category with the set of all orientations of E. This result was stated originally in a slightly different form by G. Vezzosi in arXiv:math/0004050v2 [math.AG].

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I. Panin, K. Pimenov, O. Röndigs. 2007-09-26. A universality theorem for Voevodsky's algebraic cobordism spectrum. https://arxiv.org/abs/0709.4116

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