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We show Poincar\'e Duality for $\mathbf{F}_p$-\'etale cohomology of a smoothproper rigid space over a $p$-adic field $K$. It positively answers thequestion raised by P. Scholze in his paper ``p-adic Hodge Theory forRigid-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. Themain work is duality with $\mathbf{F}_p$-coefficients.

Mod-p Poincar\'e Duality in p-adic Analytic Geometry