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On the algebraic cobordism spectra MSL and MSp

Abstract : We construct algebraic cobordism spectra MSL and MSp. They are commutative monoids in the category of symmetric T^{2}- spectra. The spectrum MSp comes with a natural symplectic orientation given either by a tautological Thom class th^{MSp} in MSp^{4,2}(MSp_{2}), a tautological Pontryagin class p_{1}^{MSp} in MSp^{4,2}(HP^{\infty}) or any of six other equivalent structures. For a commutative monoid E in the category SH(S) we prove that assignment g -> g(th^{MSp}) identifies the set of homomorphisms of monoids g : MSp -> E in the motivic stable homotopy category SH(S) with the set of tautological Thom elements of symplectic orientations of E. A weaker universality result is obtained for MSL and special linear orientations.
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Preprints, Working Papers, ...
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Contributor : Charles Walter <>
Submitted on : Wednesday, November 3, 2010 - 4:07:53 PM
Last modification on : Wednesday, October 14, 2020 - 4:23:16 AM

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  • HAL Id : hal-00531731, version 1
  • ARXIV : 1011.0651



Ivan Panin, Charles Walter. On the algebraic cobordism spectra MSL and MSp. 2010. ⟨hal-00531731⟩



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