The Borel character

Frédéric Déglise; Jean Fasel

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arXiv · 1903.11679

The Borel character

Frédéric Déglise·Jean Fasel

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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.

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Frédéric Déglise, Jean Fasel. 2019-03-27. The Borel character. https://arxiv.org/abs/1903.11679

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