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Let $R$ be the henselization of a local ring of a semistable family over thespectrum of a discrete valuation ring of mixed characteristic $(0, p)$ and $k$the residue field of $R$. In this paper, we prove an isomorphism of \'{e}talehypercohomology groups $\operatorname{H}^{n+1}_{\mathrm{\acute{e}t}}(R,\mathfrak{T}_{r}(n)) \simeq \operatorname{H}^{1}_{\mathrm{\acute{e}t}}(k,W_{r}\Omega_{\log}^{n})$ for any integers $n\geq 0$ and $r>0$ where$\mathfrak{T}_{r}(n)$ is the $p$-adic Tate twist and $W_{r}\Omega_{\log}^{n}$is the logarithmic Hodge-Witt sheaf. As an application, we prove thelocal-global principle for Galois cohomology groups over function fields ofcurves over an excellent henselian discrete valuation ring of mixedcharacteristic.

On \'{e}tale hypercohomology of henselian regular local rings with values in $p$-adic \'{e}tale Tate twists