Cohomology of p-adic Stein spaces
Cohomology of p-adic Stein spaces
复制标题
p-adic Stein 空间的上同调
DOI：
10.1007/s00222-019-00923-z
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发表时间：
2018
影响因子：
3.1
通讯作者：
Wiesława Nizioł
中科院分区：
文献类型：
--
作者：
Pierre Colmez;G. Dospinescu;Wiesława Nizioł
我们计算了Drinfeld半空间的p-adic tale和pro-tale上同调。在pro-étale情形下，主要输入是p-adic Stein空间的比较定理;这里涉及的上同调群比以前所有工作中考虑的代数簇或真解析空间的étale上同调群要大得多。在étale的情况下，经典的p-adic比较定理允许我们传递到积分微分形式上同调的计算，这是可以做到的，因为德林费尔德半空间的标准形式模型是pro-ordinary的，它们的微分形式是非循环的。
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.