Duality for Arithmetic $p$-adic Pro-étale Cohomology of Analytic Spaces

Let $K$ be a finite extension of ${\mathbb{Q}}_p$. We prove that the arithmetic $p$-adic pro-étale cohomology of smooth partially proper spaces over $K$ satisfies a duality, as conjectured by Colmez, Gilles and Nizioł. We derive it from the geometric duality on the Fargues-Fontaine curve by Galois descent techniques of Fontaine.