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Arithmetic duality for $p$-adic pro-\'etale cohomology of analytic curves
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abstract
We prove a Poincar\'e duality for arithmetic $p$-adic pro-\'etale cohomology of smooth dagger curves over finite extensions of ${\mathbf Q}_p$. 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 Poincar\'e duality (showing that it behaves like a proper smooth analytic variety of dimension $1/2$). Along the way we study functional analytic properties of arithmetic $p$-adic pro-\'etale cohomology and prove that the usual cohomology is nuclear Fr\'echet and the compactly supported one -- of compact type.
Forward citations
Cited by 2 Pith papers
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Bernstein-Zelevinsky duality for locally analytic principal series representations
For locally algebraic integral weights, the Bernstein-Zelevinsky dual of a locally analytic principal series representation equals another locally analytic principal series built from the dual Verma module and the smo...
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Compactly supported $p$-adic pro-\'etale cohomology of analytic varieties
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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