We show that the motivic spectrum representing algebraic -theory is a localization of the suspension spectrum of , and similarly that the motivic spectrum representing periodic algebraic cobordism is a localization of the suspension spectrum of . In particular, working over and passing to spaces of -valued points, we obtain new proofs of the topological versions of these theorems, originally due to the second author. We conclude with a couple of applications: first, we give a short proof of the motivic Conner-Floyd theorem, and second, we show that algebraic -theory and periodic algebraic cobordism are motivic spectra.
Cite this article
David Gepner, Victor Snaith, On the motivic spectra representing algebraic cobordism and algebraic -theory. Doc. Math. 14 (2009), pp. 359–396DOI 10.4171/DM/276