  As an extension of an author's previous research, we prove the Gersten's
conjecture for the $p$-torsion subgroup of the generalized Brauer group over a
henselian regular local ring of mixed characteristic $(0, p)$. We also prove
the $\mathbb{P}_{1}$-homotopy theorem for the generalized Brauer group which is
an extension of a result due to Auel-Bigazzi-B\"{o}hning-Graf von Bothmer in
some sense.
