Ivan Panin and Charles Walter: On the algebraic cobordism spectra MSL and MSp

paniniv@gmail.com, Charles.Walter@unice.fr

Submission: 2010, Nov 2

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.

2000 Mathematics Subject Classification: 14F42, 19G38, 19E20, 19E08

Keywords and Phrases: Algebraic symplectic cobordism, algebraic special linear cobordism, motivic symmetric spectra, symplectically oriented cohomology theories, universality.

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