On the relation of symplectic algebraic cobordism to hermitian K-theory

2010/11/02 by Ivan Panin, Panin, Ivan, Charles Walter +1
Mathematics · #14F42 #19E08 #19E20 #19G38 #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #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.1011.0652

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 reconstruct hermitian K-theory via algebraic symplectic cobordism. In the motivic stable homotopy category SH(S) there is a unique morphism g : MSp -> BO of commutative ring T- spectra which sends the Thom class th^MSp to the Thom class th^BO. We show that the induced morphism of bigraded cohomology theories MSp^*,* -> BO^*,* is isomorphic to the morphism of bigraded cohomology theories obtained by applying to MSp^*,* the "change of (simply graded) coefficients rings" MSp^4*,2* -> BO^4*,2*. This is an algebraic version of the theorem of Conner and Floyd reconstructing real K-theory via symplectic cobordism.

Citations

• On the motivic commutative ring spectrum BO
• On the algebraic cobordism spectra MSL and MSp

Related

• On the relation of special linear algebraic cobordism to Witt groups
• Derived Algebraic Cobordism
• Algebraic cobordism
• On the motivic commutative ring spectrum BO
• On the algebraic cobordism spectra MSL and MSp