On the algebraic cobordism spectra MSL and MSp

Ivan Panin; Charles Walter

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arXiv · 1011.0651

On the algebraic cobordism spectra MSL and MSp

Ivan Panin·Charles Walter

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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 Borel class b_{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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Ivan Panin, Charles Walter. 2010-11-02. On the algebraic cobordism spectra MSL and MSp. https://arxiv.org/abs/1011.0651

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