2012/06/26 by Amalendu Krishna, Krishna, Amalendu
Mathematics · #14F43 (Primary) 55N22 (Secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #msc:14F43 #msc:55N22
paper · pdf · doi:10.48550/arxiv.1206.5952
Preliminary version
arxiv created 2012/06/26 · openalex publication_date 2012/06/26 · arxiv updated 2012/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a linear algebraic group G over a field k, we define an equivariant version of the Voevodsky's motivic cobordism MGL. We show that this is an oriented cohomology theory with localization sequence on the category of smooth G-schemes and there is a natural transformation from this functor to the functor of equivariant motivic cohomology. We give several applications. In particular, we use this equivariant motivic cobordism to study the cobordism ring of the classifying spaces and the cycle class maps from the algebraic to the singular cohomology of such spaces. This theory of motivic cobordism allows us to define the theory of motivic cobordism on the category of all smooth quotient stacks.