  We show Poincar\'e Duality for $\mathbf{F}_p$-\'etale cohomology of a smooth
proper rigid space over a $p$-adic field $K$. It positively answers the
question raised by P. Scholze in his paper ``p-adic Hodge Theory for
Rigid-analytic varieties''. We also show versions of Poincar\'e Duality for
$\mathbf{Z}/p^n\mathbf{Z}$, $\mathbf{Z}_p$, and $\mathbf{Q}_p$-cofficients. The
main work is duality with $\mathbf{F}_p$-coefficients.

Algebraic Geometry;Number Theory