On the Whitehead theorem for nilpotent motivic spaces

2022/10/12 by Asok, Aravind, Bachmann, Tom, Hopkins, Michael J. · 3 citations
#14F42 20F19 55S45 #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.2210.05933

Abstract

We improve some foundational connectivity results and the relative Hurewicz theorem in motivic homotopy theory, study functorial central series in motivic local group theory, establish the existence of functorial Moore--Postnikov factorizations for nilpotent morphisms of motivic spaces under a mild technical hypothesis and establish an analog of the Whitehead theorem for nilpotent motivic spaces. As an application, we deduce a surprising unstable motivic periodicity result.

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• Comparison of motives with rational coefficients
• Efficient generation of projective modules: a motivic view
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