Beilinson–Lichtenbaum-type comparison over the rationals

Let $\alpha^*$ be the inverse-image functor from etale to Zariski motivic complexes, let $j^*{\Bbb Z}_l(n)_S$ be the indicated arithmetic etale Tate-twist complex, and let $n\ge0$. Rational comparison conjecture. The map

$$\alpha^*{\Bbb Z}(n)\otimes {\Bbb Z}_l\to \tau_{\le n}j^*{\Bbb Z}_l(n)_S$$

restricted to smooth varieties over ${\Bbb Q}$ is an isomorphism. This is proposed as a characteristic-zero comparison statement following the preceding conjectural results.