Geodesic
On the motivic spectra representing algebraic cobordism and algebraic $K$-theory
Documenta mathematica, Tome 14 (2009), pp. 359-396.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We show that the motivic spectrum representing algebraic $K$-theory is a localization of the suspension spectrum of $\mathbb{P}^\infty$, and similarly that the motivic spectrum representing periodic algebraic cobordism is a localization of the suspension spectrum of $BGL$. In particular, working over $\mathbb{C}$ and passing to spaces of $\mathbb{C}$-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 $E_\infty$ motivic spectra.
Classification : 55N15, 55N22 
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     title = {On the motivic spectra representing algebraic cobordism and algebraic $K$-theory},
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Gepner, David; Snaith, Victor. On the motivic spectra representing algebraic cobordism and algebraic $K$-theory. Documenta mathematica, Tome 14 (2009), pp. 359-396. http://geodesic.mathdoc.fr/item/DOCMA_2009__14__a14/