The Gersten conjecture for p-adic tame Tate twists

Let $X$ be a smooth scheme over $S$ of dimension $d$. Write $X^{(a)}$ for the points of codimension $a$, $i_{*,x}$ for extension by zero from $x$, $\epsilon$ for the relevant morphism of sites, and $\mathcal T_r^t(m)$ for the $p$-adic tame Tate twist. Gersten conjecture. The complex of sheaves

$$0\to R^n\epsilon_*\mathcal T_r^t(m)\to\bigoplus_{x\in X^{(0)}}i_{*,x}H^q(k(x),\mathcal T_r^t(m))\to\bigoplus_{x\in X^{(1)}}i_{*,x}H^{q-1}(k(x),\mathcal T_r^t(m-1))\to$$ $$\cdots\to\bigoplus_{x\in X^{(d)}}i_{*,x}H^{q-d}(x,\mathcal T_r^t(m-d))\to0$$

is exact in the Nisnevich topology.

This is the Gersten conjecture for $p$-adic tame Tate twists. The source says it is known for $p$-adic etale Tate twists and that the displayed conjecture holds for $n\leq m$ by the Beilinson–Lichtenbaum conjecture and a cited theorem; the general case remains open.