The etale realization conjecture for motivic complexes over finite fields

Let $p$ be a prime, let $l$ be a prime distinct from $p$, and let $\alpha^*$ denote passage from the etale to the underlying motivic setting. For each integer $n$, there is a morphism

$${\Bbb Z}_l(0)^c\operatornamewithlimits\otimes^L\alpha^*{\Bbb Z}(n)\to {\Bbb Z}_l(n)^c.$$

Etale realization conjecture. This morphism is an isomorphism. Equivalently, after tensoring with ${\Bbb Q}$, the induced morphism is an isomorphism. The mod-$l$ reduction is already known to be an isomorphism, so the conjecture concerns the integral or rational comparison between motivic and continuous etale complexes.