2019/03/27 by Frédéric Déglise, Déglise, Frédéric, Jean Fasel +1
Mathematics · #11E70 #11E81 #14F42 #19G38 #19L10 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:11E70 #msc:11E81 #msc:14F42 #msc:19G38 #msc:19L10
paper · pdf · doi:10.48550/arxiv.1903.11679
Major changes. Comments are still welcome!
arxiv created 2020/04/10 · arxiv updated 2020/04/13
The main purpose of this article is to define a quadratic analog of the Chern character, the so-called Borel character, which identifies rational higher Grothendieck-Witt groups with a sum of rational MW-motivic cohomologies and rational motivic cohomologies. We also discuss the notion of ternary laws due to Walter, a quadratic analog of formal group laws, and compute what we call the additive ternary laws, associated with MW-motivic cohomology. Finally, we provide an application of the Borel character by showing that the Milnor-Witt K-theory of a field F embeds into suitable higher Grothendieck-Witt groups of F modulo explicit torsion.