Cohomology of p-adic Stein spaces

We compute p -adic étale and pro-étale cohomologies of Drinfeld half-spaces. In the pro-étale case, the main input is a comparison theorem for p -adic Stein spaces; the cohomology groups involved here are much bigger than in the case of étale cohomology of algebraic varieties or proper analytic spac...

Full description

Saved in:
Bibliographic Details
Published in:Inventiones mathematicae 2020-03, Vol.219 (3), p.873-985
Main Authors: Colmez, Pierre, Dospinescu, Gabriel, Nizioł, Wiesława
Format: Article
Language:English
Subjects:
Half spaces
Homology
Mathematics
Mathematics and Statistics
Theorems
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We compute p -adic étale and pro-étale cohomologies of Drinfeld half-spaces. In the pro-étale case, the main input is a comparison theorem for p -adic Stein spaces; the cohomology groups involved here are much bigger than in the case of étale cohomology of algebraic varieties or proper analytic spaces considered in all previous works. In the étale case, the classical p -adic comparison theorems allow us to pass to a computation of integral differential forms cohomologies which can be done because the standard formal models of Drinfeld half-spaces are pro-ordinary and their differential forms are acyclic.
ISSN:0020-9910
1432-1297
DOI:10.1007/s00222-019-00923-z