Let $X$ be a smooth variety over a field.

Is there a spectral sequence:

$$E_1^{p,q} := \bigoplus_{x\in X^{(p)}}H^{q-p}(\kappa(x)_{\rm ét},\mathbf{Z}(n))\Rightarrow H^{q-p}(X_{\rm ét},\mathbf{Z}(n))$$

with the abutement being **étale** motivic cohomology?

Here is my guess: since after rationalizing, $H^{r}(*,\mathbf{Q}(n)) = H^r(*_{\rm ét},\mathbf{Q}(n))$, one can invoke the known analog of the above spectral sequence for usual motivic cohomology, rationally.

One is then reduced to show this for mod $\ell^t$ étale motivic cohomology, which is, depending on $\ell$, either $(\mathbf{Z}/\ell^t)(n)$ étale cohomology, or level $p^t$ logarithmic de Rham Witt cohomology.

For both, the result is true.

So my expectation is that this is true and has been shown in the literature. Any reference, please?