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arXiv · 2012.02351

Detecting motivic equivalences with motivic homology

David Hemminger
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Abstract

Let $k$ be a field, let $R$ be a commutative ring, and assume the exponential characteristic of $k$ is invertible in $R$. In this note, we prove that isomorphisms in Voevodsky's triangulated category of motives $\mathcal{DM}(k;R)$ are detected by motivic homology groups of base changes to all separable finitely generated field extensions of $k$. It then follows from previous conservativity results that these motivic homology groups detect isomorphisms between certain spaces in the pointed motivic homotopy category $\mathcal{H}(k)_*$.

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David Hemminger. 2020-12-04. Detecting motivic equivalences with motivic homology. https://arxiv.org/abs/2012.02351

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