Detecting motivic equivalences with motivic homology

Hemminger, David

doi:10.1090/bproc/82

Detecting motivic equivalences with motivic homology
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by David Hemminger HTML | PDF

Proc. Amer. Math. Soc. Ser. B 9 (2022), 180-185

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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