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THE BOREL CHARACTER

Published online by Cambridge University Press:  26 July 2021

Frédéric Déglise
Affiliation:
ENS de Lyon, UMPA, CNRS, 46 allée d’Italie, 69364 Lyon Cedex 07, France, (frederic.deglise@ens-lyon.fr) URL: http://perso.ens-lyon.fr/frederic.deglise/
Jean Fasel
Affiliation:
Institut Fourier - UMR 5582, Université Grenoble-Alpes, CS 40700, 38058 Grenoble Cedex 9, France (Jean.Fasel@univ-grenoble-alpes.fr), URL: https://www-fourier.ujf-grenoble.fr/∼faselj/

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.

Type
Research Article
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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