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

Detecting motivic equivalences with motivic homology