English

The Borel character

Algebraic Geometry 2020-04-13 v2

Abstract

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.

Keywords

Cite

@article{arxiv.1903.11679,
  title  = {The Borel character},
  author = {Frédéric Déglise and Jean Fasel},
  journal= {arXiv preprint arXiv:1903.11679},
  year   = {2020}
}

Comments

Major changes. Comments are still welcome!

R2 v1 2026-06-23T08:21:30.220Z