Geodesic
On the motivic spectra representing algebraic cobordism and algebraic $K$-theory
Documenta mathematica, Tome 14 (2009), pp. 359-396
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We show that the motivic spectrum representing algebraic K-theory is a localization of the suspension spectrum of P∞, and similarly that the motivic spectrum representing periodic algebraic 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.
DOI : 10.4171/dm/276
Classification : 55N15, 55N22 
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     title = {On the motivic spectra representing algebraic cobordism and algebraic $K$-theory},
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     year = {2009},
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Victor Snaith; David Gepner. On the motivic spectra representing algebraic cobordism and algebraic $K$-theory. Documenta mathematica, Tome 14 (2009), pp. 359-396. doi: 10.4171/dm/276

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