A universality theorem for Voevodsky's algebraic cobordism spectrum

Panin, I.; Pimenov, K.; Röndigs, O.

A universality theorem for Voevodsky's algebraic cobordism spectrum

Authors

Panin, I.

Pimenov, K.

Röndigs, O.

Description

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].
LaTeX, 14 pages, uses XY-pic