A UNIVERSALITY THEOREM FOR VOEVODSKY'S ALGEBRAIC COBORDISM SPECTRUM

Abstract

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 P-1-spectra, equipped with the symmetric monoidal structure described in [7]. The algebraic cobordism P-1-spectrum MGL is considered as a commutative monoid equipped with a canonical orientation th(MGL) is an element of MGL(2,1)(Th(O(-1))). For a commutative monoid E in the category SH(S), it is proved that the assignment phi bar right arrow phi(th(MGL)) identifies the set of monoid homomorphisms phi: 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].