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

2018/04/13 by Asok, Aravind, Fasel, Jean, Williams, Ben
#14F42 19B14 19D45 20J05 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #Group Theory (math.GR) #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1804.05030

Abstract

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 A¹-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 A¹-homotopy sheaf of the general linear group to the stable \mathbb A¹-homotopy of motivic spheres.

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