| Résume | Let $K$ be a finite extension of $\mathbb{Q}_p$. We prove that the arithmetic $p$-adic pro-etale cohomology of smooth partially proper spaces over $K$ satisfies a duality, as conjectured by Colmez-Gilles-Niziol. I will begin by providing some motivation for this question. Then I will explain how the cohomology is related to sheaves on the Fargues-Fontaine curve and how to deduce the result from the 'Poincare duality on the Fargues-Fontaine curve'. |
