On the motivic spectra representing algebraic cobordism and algebraic $K$-theory

Abstract

We show that the motivic spectrum representing alge- braic K-theory is a localization of the suspension spectrum of P ∞ , and similarly that the motivic spectrum representing periodic alge- braic cobordism is a localization of the suspension spectrum of BGL. In particular, working over C and passing to spaces of C-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 K-theory and periodic algebraic cobordism are E∞ motivic spectra.