Title: Duality for Arithmetic p-adic Pro-etale Cohomology of Analytic Spaces

Abstract: Let K be a finite extension of 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 start from some recent history and examples to motivate this question. Since the proof is based on Niziol's syntomic comparison theorem and the Poincare duality on the Fargues-Fontaine curve, I will also briefly mention the relation between the recent work of Anschutz-Le Bras-Mann and Anschutz-Bosco-Le Bras-Camargo-Scholze.