标题： 关于$p$-进解析群作用的上同调的一篇注记 显示英文标题

标题： A note on the cohomology of $p$-adic analytic group actions

摘要： 我们证明，给定一个紧致$p$-adic 李群在域的巴拿赫空间上的解析作用，可以从限制到一个 pro-$p$伪循环子群的相应陈述中检测出所有连续上同调群的同时消失或同时有限维性。 我们还提出一个推广此结果的猜想，在该猜想中允许基域具有混合特征，并允许子群为幂零的。 最后，我们提出了关于李代数上同调的类似猜想，并将其与Kostant的一个定理联系起来。 显示英文摘要

摘要： We prove that given an analytic action of a compact $p$-adic Lie group on a Banach space over a field of positive characteristic, one can detect either the simultaneous vanishing or the simultaneous finite-dimensionality of all of the continuous cohomology groups from the corresponding statement for the restriction to a pro-$p$ procyclic subgroup. We also formulate a conjecture generalizing this result, in which the base field is allowed to have mixed characteristic and the subgroup is allowed to be nilpotent. Finally, we formulate an analogous conjecture about Lie algebra cohomology and relate this to a theorem of Kostant.