Exactness conjecture for the higher Chow cycle-class complex

Let $K$ be a global field, let $X/K$ be a smooth projective geometrically integral variety of dimension $d$, let $n$ be prime to the characteristic of $K$, and let $i>0$. Set $j=d+1-i$, and let the prime on the product denote the restricted product of higher Chow groups. Exactness conjecture. The complex

$$\mathrm{CH}^{i}(X,a,\mathbb{Z}/n\mathbb{Z})\rightarrow \sideset{}{^{\prime}}\prod_{v\in P_K} \mathrm{CH}^{i}(X_{K_v},a,\mathbb{Z}/n\mathbb{Z})\rightarrow H^{2j+a}_{\mathrm{\acute{e}t}}(X,\mu_n^{\otimes j})^\vee$$

is exact, where $A^\vee=\operatorname{Hom}(A,\mathbb{Q}/\mathbb{Z})$.

This is the complex formulation of the preceding higher-cycle local-to-global conjecture, expressing that the only obstruction to patching local classes is the indicated étale-cohomological pairing.