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Journal Articles Journal of the Institute of Mathematics of Jussieu Year : 2021

The Borel character

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Jean Fasel


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.

Dates and versions

ensl-03466895 , version 1 (06-12-2021)



Frédéric Déglise, Jean Fasel. The Borel character. Journal of the Institute of Mathematics of Jussieu, 2021, pp.1-51. ⟨10.1017/S1474748021000281⟩. ⟨ensl-03466895⟩
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