Compositio Mathematica· 2026Q1
Arithmetic duality for p -adic pro-étale cohomology of analytic curves
- 16citations
- Q1SCImago
- 2026year
Short summary
A Poincaré duality for arithmetic p-adic pro-étale cohomology of smooth dagger curves over finite extensions of Q_p is proven, deduced from geometric comparison theorems and Tate/Serre dualities.
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Key points
- Proves Poincaré duality for arithmetic p-adic pro-étale cohomology of smooth dagger curves over finite extensions of Q_p.
- Deduces the duality via Hochschild-Serre spectral sequence from geometric comparison theorems and Tate/Serre dualities.
- Verifies product compatibility using reduction to the ghost circle, which also shows Poincaré duality.
- Studies functional analytic properties, classifying the cohomology as nuclear Fréchet and compactly supported cohomology as of compact type.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract We prove a Poincaré duality for arithmetic p -adic pro-étale cohomology of smooth dagger curves over finite extensions of bold upper Q Subscript p Q p $\mathbf{Q}_p$ . We deduce it, via the Hochschild–Serre spectral sequence, from geometric comparison theorems combined with Tate and Serre dualities. The compatibility of all the products involved is checked via reduction to the ghost circle, for which we also prove a Poincaré duality (showing that it behaves like a proper smooth analytic variety of dimension 1 divided by 2 1 / 2 $1/2$ ). Along the way we study functional analytic properties of arithmetic p -adic pro-étale cohomology and prove that the usual cohomology is nuclear Fréchet and the compactly supported one: of compact type.
The authors' abstract, as published at the source. Compositio Mathematica, 2026 · DOI ↗
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Field: Geometry and Topology
Geometry and TopologyMathematics