  In this article, we prove a $p$-adic analogue of the local invariant cycle
theorem for $H^2$ in mixed characteristics. As a result, for a smooth
projective variety $X$ over a $p$-adic local field $K$ with a proper flat
regular model $\mathcal{X}$ over $O_K$, we show that the natural map
$Br(\mathcal{X})\rightarrow Br(X_{\bar{K}})^{G_K}$ has a finite kernel and a
finite cokernel. And we prove that the natural map
$Hom(Br(X)/Br(K)+Br(\mathcal{X}), \mathbb{Q}/\mathbb{Z}) \rightarrow Alb_X(K)$
has a finite kernel and a finite cokernel, generalizing Lichtenbaum's duality
between Brauer groups and Jacobians for curves to arbitrary dimensions.
