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The Borel character

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.
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Contributor : Frédéric Déglise Connect in order to contact the contributor
Submitted on : Monday, December 6, 2021 - 11:46:13 AM
Last modification on : Tuesday, January 4, 2022 - 6:46:17 AM

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



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