Let $K/\mathbb Q_p$ be a discretely valued non-archemedean field, let $X$ be a smooth scheme over $\mathcal O_K$. To $X$ one can associate two rigid-analytic spaces over $K$:

1) the analytification $X_K^{\mathrm{an}} $ of the generic fiber,

2) the generic fiber $\mathfrak X^{\mathrm{rig}}$ of the corresponding formal scheme $\mathfrak X$.

One has a natural map $i_X:\mathfrak X^{\mathrm{rig}}\rightarrow X_K^{\mathrm{an}}$ which is an open immersion and an isomorphism in the case of proper $X$. For any $X$ one also has a comparison isomorphism between etale cohomology groups of $X_{\overline K}$ and $X_{K}^{\mathrm{an}}$ for torsion coefficients. So in the proper case one also has an isomorphism $H^i(({X_K})_{et},\mathbb Z/n\mathbb Z)\simeq H^i(\mathfrak X^{\mathrm{rig}}_{et},\mathbb Z/n\mathbb Z)$. Does one have this isomorphism in general or it holds only for $X$ proper? If not what could be a counterexample?