Mod-p Poincaré Duality in p-adic analytic geometry

We show Poincar\'e Duality for Fₚ-\'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 /pⁿ, ₚ, and ₚ-cofficients. The main work is duality with Fₚ-coefficients.