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Pré-Publication, Document De Travail Année : 2021

Motivic spheres and the image of the Suslin--Hurewicz map

Jean Fasel
Aravind Asok
  • Fonction : Auteur
Ben Williams
  • Fonction : Auteur

Résumé

We show that an old conjecture of A.A. Suslin characterizing the image of a Hurewicz map from Quillen K-theory in degree $n$ to Milnor K-theory in degree $n$ admits an interpretation in terms of unstable ${\mathbb A}^1$-homotopy sheaves of the general linear group. Using this identification, we establish Suslin's conjecture in degree $5$ for infinite fields having characteristic unequal to $2$ or $3$. We do this by linking the relevant unstable ${\mathbb A}^1$-homotopy sheaf of the general linear group to the stable ${\mathbb A}^1$-homotopy of motivic spheres.

Dates et versions

hal-03470525 , version 1 (08-12-2021)

Identifiants

Citer

Jean Fasel, Aravind Asok, Ben Williams. Motivic spheres and the image of the Suslin--Hurewicz map. 2021. ⟨hal-03470525⟩

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