COHOMOLOGY OF p-ADIC STEIN SPACES

We compute the p-adic étale and the pro-etale cohomologies of the Drinfeld half-space of any dimension. The main input is a new comparison theorem for the p-adic pro-étale cohomology of p-adic Stein spaces. On calcule les cohomologies étale et pro-étale p-adiques de l'espace de Drinfeld en dime...

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Bibliographic Details
Published in:Inventiones mathematicae 2019
Main Authors: Colmez, Pierre, Dospinescu, Gabriel, Niziol, Wieslawa
Format: Article
Language:English
Subjects:
Mathematics
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Summary:We compute the p-adic étale and the pro-etale cohomologies of the Drinfeld half-space of any dimension. The main input is a new comparison theorem for the p-adic pro-étale cohomology of p-adic Stein spaces. On calcule les cohomologies étale et pro-étale p-adiques de l'espace de Drinfeld en dimension arbitraire. L'ingrédient principal est un nouveau théorème de comparaison pour la cohomologie pro-étale des espaces de Stein p-adiques.
ISSN:0020-9910
1432-1297