Lichtenbaum's finiteness conjecture for étale motivic cohomology

Let $X$ be an arithmetic scheme, meaning a separated scheme of finite type over $\operatorname{Spec}\mathbb{Z}$, and let $n<0$. Write $X_{\text{ét}}$ for its étale site and $\mathbb{Z}^c(n)$ for the dimension-$n$ motivic complex. Lichtenbaum's finiteness conjecture. The groups

$$H^i(X_{\text{ét}},\mathbb{Z}^c(n))$$

should be finitely generated for every $i\in\mathbb{Z}$. This finiteness assumption underlies the construction of Weil-étale cohomology for arbitrary arithmetic schemes and is used throughout the paper; the source does not provide a resolution.