We discuss several points in the approaches of Faltings and Scholze to $p$-adic Hodge theory and Grothendieck duality in this context. Let $K$ be an algebraically closed complete rank 1 valued field with valuation ring $O_{K}$ of mixed characteristic $(0,p), X$ a proper smooth connected rigid analytic space over $K$ of dimension $d$ with normal formal model $\mathcal{X}$ over Spf $O_{K}$. To show Poincaré duality for $H^{_}(X_{\mathrm{e}\mathrm{t}},\ \mathbb{Z}/p)$ one considers the ``nearby cycle'' complex $R\psi_{_}(O^{+}/p)$ on $\mathcal{X}/p$; it has bounded almost coherent cohomology and one observes that $\mathcal{H}^{d}R\psi_{*}(d)$ has a canonical almost map to the dualizing sheaf: we show that this induces an almost autoduality by means of local uniformization by quotients of nice formal models by finite groups.