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2008 A universality theorem for Voevodsky's algebraic cobordism spectrum
Ivan Panin, Konstantin Pimenov, Oliver Röndigs
Homology Homotopy Appl. 10(2): 211-226 (2008).

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 $\mathbb{P}^1$-spectra, equipped with the symmetric monoidal structure described in [7]. The algebraic cobordism $\mathbb{P}^1$-spectrum MGL is considered as a commutative monoid equipped with a canonical orientation$th^{MGL} \in \rm{MGL}^{2,1}(\rm{Th}(\mathcal{O}(-1)))$. For a commutative monoid $E$ in the category SH($S$), it is proved that the assignment $\varphi \longmapsto \varphi(th^{\rm{MGL}})$ identifies the set of monoid homomorphisms $\varphi : \rm {MGL} \longmapsto E$ 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].

Citation

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Ivan Panin. Konstantin Pimenov. Oliver Röndigs. "A universality theorem for Voevodsky's algebraic cobordism spectrum." Homology Homotopy Appl. 10 (2) 211 - 226, 2008.

Information

Published: 2008
First available in Project Euclid: 1 September 2009

zbMATH: 1162.14013
MathSciNet: MR2475610

Subjects:
Primary: 14F05, 55N22, 55P43

Rights: Copyright © 2008 International Press of Boston

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