The Hurewicz map in motivic homotopy theory

For an $𝔸^{1}$ -connected pointed simplicial sheaf $𝒳$ over a perfect field $k$ , we prove that the Hurewicz map $π_{1}^{𝔸^{1}} (𝒳) \to H_{1}^{𝔸^{1}} (𝒳)$ is surjective. We also observe that the Hurewicz map for $ℙ_{k}^{1}$ is the abelianization map. In the course of proving this result, we also show that for any morphism $ϕ$ of strongly $𝔸^{1}$ -invariant sheaves of groups, the image and kernel of $ϕ$ are also strongly $𝔸^{1}$ -invariant.

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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

Vol. 7, No. 1, 2022

Utsav Choudhury and Amit Hogadi

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors