Let G be a reductive split p-adic group and let U be the unipotent radical of a Borel subgroup. We study the cohomology with trivial ${\mathbb{Z}}_p$-coefficients of the profinite nilpotent group $N=\mathrm{U}({\mathcal{O}}_F)$ and its Lie algebra $\mathfrak{n},$ by extending a classical result of Kostant to our integral p-adic setup. The techniques used are a combination of results from group theory, algebraic groups and homological algebra.

中文翻译：

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关于积分p-adic单能根的同调

令G为还原性分裂p- adic基团，令U为Borel子群的单能根。我们研究琐碎的同调${\mathbb{ž}}_p$幂等群的系数 $ñ=\mathrm{ü}（{\mathcal{Ø}}_F）$ 及其李代数 $\mathfrak{ñ}，$通过将Kostant的经典结果扩展到我们的积分p -adic设置。所使用的技术是群论，代数群和同源代数的结果的组合。