THE BOREL CHARACTER. (26th March 2023)

• Record Type: Journal Article
• Authors: Déglise, Frédéric; Fasel, Jean
• Is Part Of: Journal of the Institute of Mathematics of Jussieu. Volume 22:Number 2(2023)
• Page Start: 747
• Page End: 797
• Publication Date: 2023-03-26
• Subjects: motivic homotopy theory -- Hermitian K-theory -- MW-motivic cohomology -- characteristic classes; 19E15 -- 19E20 -- 19E99 -- 19G38 -- 19G99 -- 11E04 -- 11E39 -- 11E70 -- 11E81; Mathematics -- Periodicals; 510.5
• DOI: 10.1017/S1474748021000281
• Languages: English
• ISSNs: 1474-7480

Abstract

Abstract: The main purpose of this article is to define a quadratic analogue of the Chern character, the so-called Borel character, that identifies rational higher Grothendieck-Witt groups with a sum of rational Milnor-Witt (MW)-motivic cohomologies and rational motivic cohomologies. We also discuss the notion of ternary laws due to Walter, a quadratic analogue 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.