On the algebraic cobordism spectra MSL and MSp

2010/11/02 by Ivan Panin, Panin, Ivan, Charles Walter +1 · 2 citations
Mathematics · #14F42 #19E08 #19E20 #19G38 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #math.AG #math.KT #msc:14F42 #msc:19E08 #msc:19E20 #msc:19G38

paper · pdf · doi:10.48550/arxiv.1011.0651

openalex publication_date 2010/11/02 · arxiv created 2018/03/12 · arxiv updated 2018/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct algebraic cobordism spectra MSL and MSp. They are commutative monoids in the category of symmetric T²- spectra. The spectrum MSp comes with a natural symplectic orientation given either by a tautological Thom class th^MSp in MSp^4,2(MSp₂), a tautological Borel class b₁^MSp in MSp^4,2(HP^∞) 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.

Citations

• Quaternionic Grassmannians and Borel classes in algebraic geometry

Cited by

• On the relation of symplectic algebraic cobordism to hermitian K-theory
• Fundamental classes in motivic homotopy theory

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