动机同伦理论中的Hurewicz映射

IF 0.5 Q3 MATHEMATICS Annals of K-Theory Pub Date : 2021-01-05 DOI:10.2140/akt.2022.7.179

Utsav Choudhury, A. Hogadi

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引用次数: 6

摘要

．对于完美域k上的a1连通点简单束X，证明了Hurewicz映射π a11 (X)→H a11 (X)是满射。我们还观察到p1k的Hurewicz图是阿贝尔化图。在证明这一结果的过程中，我们还证明了对于群的强a1不变簇的任何态射φ， φ的像和核也是强a1不变的。

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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 A 1 1 ( X ) → H A 1 1 ( X ) is surjective. We also observe that the Hurewicz map for P 1 k is the abelianisation 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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