Beilinson–Lichtenbaum generalized Hilbert 90 conjecture for motivic cohomology

Let $k$ be a field and let $n\ge 0$. The motivic complex ${\bf Z}(n)$ is evaluated on $\operatorname{Spec}(k)$ in the étale topology. Beilinson–Lichtenbaum's generalized Hilbert 90 conjecture. For every field $k$ and every $n\ge 0$, one has

$${\bf H}^{n+1}_{et}(\operatorname{Spec}(k),{\bf Z}(n))=0.$$

This conjecture is a fundamental property expected of motivic complexes and is the main conjectural input behind the Beilinson–Lichtenbaum comparison results. The paper proves its 2-local version, but the statement as written is not resolved by the supplied text.