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Duality for Arithmetic $p$-adic Pro-étale Cohomology of Analytic Spaces (2412.11786v3)
Published 16 Dec 2024 in math.AG and math.NT
Abstract: 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 and Nizio{\l}. We derive it from the geometric duality on the Fargues-Fontaine curve by Galois descent techniques of Fontaine.
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