Cohomology of p-adic Stein spaces

• 成果类型: Article
• 署名作者: Colmez, Pierre; Dospinescu, Gabriel; Niziol, Wieslawa
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Ecole Normale Superieure de Lyon (ENS de LYON)
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-019-00923-z
• 发表日期: 2020
• 页码: 873-985
• 关键词: jordan-holder series; etale cohomology; analytic spaces; sequence; HOMOLOGY; THEOREM; forms

摘要

We compute p-adic etale and pro-etale cohomologies of Drinfeld half-spaces. In the pro-etale 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 etale cohomology of algebraic varieties or proper analytic spaces considered in all previous works. In the etale 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.