Vol. 7, No. 1, 2022

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The Hurewicz map in motivic homotopy theory

Utsav Choudhury and Amit Hogadi

Vol. 7 (2022), No. 1, 179–190
Abstract

For an 𝔸1-connected pointed simplicial sheaf 𝒳 over a perfect field k, we prove that the Hurewicz map π1𝔸1 (𝒳) H1𝔸1 (𝒳) is surjective. We also observe that the Hurewicz map for k1 is the abelianization map. In the course of proving this result, we also show that for any morphism ϕ of strongly 𝔸1-invariant sheaves of groups, the image and kernel of ϕ are also strongly 𝔸1-invariant.

Keywords
Hurewicz map, motivic homotopy theory
Mathematical Subject Classification
Primary: 14F42
Milestones
Received: 24 June 2021
Revised: 8 November 2021
Accepted: 13 December 2021
Published: 20 June 2022
Authors
Utsav Choudhury
Department of Mathematics
Statistics and Mathematics Unit, Indian Statistical Institute
Kolkata
India
Amit Hogadi
Department of Mathematics
IISER Pune
Pune
India