De Rham comparison and Poincaré duality for rigid varieties

2019/12/30 by Lan, Kai-Wen, Liu, Ruochuan, Zhu, Xinwen · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1912.13030

Abstract

Over any smooth algebraic variety over a p-adic local field k, we construct the de Rham comparison isomorphisms for the étale cohomology with partial compact support of de Rham \mathbb Z_p-local systems, and show that they are compatible with Poincaré duality and with the canonical morphisms among such cohomology. We deduce these results from their analogues for rigid analytic varieties that are Zariski open in some proper smooth rigid analytic varieties over k. In particular, we prove finiteness of étale cohomology with partial compact support of any \mathbb Z_p-local systems, and establish the Poincaré duality for such cohomology after inverting p.

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• Irreducibility of Newton strata in Picard modular surfaces and split local Galois representations
• Locally analytic completed cohomology of Shimura varieties of Hodge type

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