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 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.

References in corpus (2)

• Algebraic cobordism
• Brown-Peterson spectra in stable A^1-homotopy theory

Cited by in corpus (6)

• Fundamental classes in motivic homotopy theory
• A^1-Euler classes: six functors formalisms, dualities, integrality and linear subspaces of complete intersections
• Framed transfers and motivic fundamental classes
• Stable operations and cooperations in derived Witt theory with rational coefficients
• The unit map of the algebraic special linear cobordism spectrum
• Algebraic elliptic cohomology and flops II: $SL$-cobordism