Beilinson–Lichtenbaum comparison conjecture for motivic cohomology

Let $X$ be a smooth variety over a field $k$, and let $p,q$ be integers. Consider the canonical map from motivic cohomology in the Zariski topology to motivic cohomology in the étale topology,

$${\bf H}^{p}_{Zar}(X,{\bf Z}(q))\longrightarrow {\bf H}^{p}_{et}(X,{\bf Z}(q)).$$

Beilinson–Lichtenbaum comparison conjecture. This map is an isomorphism for $p\le q+1$.

The conjecture is described as a consequence of generalized Hilbert 90 and implies the norm residue conjecture. The supplied text does not state a resolution status for this formulation.