Motivic spheres and the image of the Suslin--Hurewicz map - Archive ouverte HAL
Article Dans Une Revue Inventiones Mathematicae Année : 2019

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

Aravind Asok
  • Fonction : Auteur
Jean Fasel
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

Aravind Asok, Jean Fasel, Ben Williams. Motivic spheres and the image of the Suslin--Hurewicz map. Inventiones Mathematicae, 2019, 219 (1), pp.39-73. ⟨10.1007/s00222-019-00907-z⟩. ⟨hal-03470525⟩
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