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Duality for Arithmetic $p$-adic Pro-\'etale Cohomology of Analytic Spaces

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arxiv 2412.11786 v3 pith:T4NJ5CPX submitted 2024-12-16 math.AG math.NT

Zhenghui Li This is my paper · ORCID
classification math.AGmath.NT
keywords dualityadicarithmeticcohomologyetalepro-spacesanalytic
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A 6-functor formalism for solid quasi-coherent sheaves on the Fargues-Fontaine curve

    math.AG 2024-12 accept novelty 7.0 of 10

    A 6-functor formalism for Z_p-linear solid quasi-coherent sheaves on small v-stacks is constructed, yielding Poincare duality for pro-etale Q_p-cohomology.

  2. Compactly supported $p$-adic pro-\'etale cohomology of analytic varieties

    math.AG 2025-01 conditional novelty 6.0 of 10

    Defines compactly supported p-adic pro-étale cohomology for partially proper rigid analytic varieties and proves a stable-range comparison with syntomic cohomology.

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