Semi-topological Quillen-Lichtenbaum conjecture for coherent sheaves

Let $X$ be a separated scheme over $\mathbb{C}$ of finite type and let $A$ be an abelian group. The semi-topological Quillen-Lichtenbaum conjecture for coherent sheaves. The canonical map

$$K^{\mathrm{st}}_n(\operatorname{coh}(X),A)\to K^{\mathrm{top}}_n(\operatorname{coh}(X),A)$$

is an isomorphism for $n\geq\dim X-1$ and a monomorphism for $n=\dim X-2$. This is the coherent-sheaf version of the semi-topological comparison; the source states it as a conjecture and gives no resolution.