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

2024/12/16 by Zhenghui Li, Li, Zhenghui
Mathematics · #14F30 #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2412.11786

openalex publication_date 2024/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

Let K be a finite extension of 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.

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