Arithmetic duality for p-adic pro-étale cohomology of analytic curves

2023/08/15 by Colmez, Pierre, Gilles, Sally, Nizioł, Wiesława · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2308.07712

Abstract

We prove a Poincaré duality for arithmetic p-adic pro-étale 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 Poincaré 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-étale cohomology and prove that the usual cohomology is nuclear Fréchet and the compactly supported one -- of compact type.

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