标题： 上同调的$p$-进Chevalley群 显示英文标题

标题： Cohomology of $p$-adic Chevalley groups

摘要： 设 $G$ 是 $\mathbf{Q}_p$ 的有限无分支扩张 $K$ 的整数环上的分裂连通约化群。 在对 $G$ 的 Coxeter 数进行标准假设的情况下，我们计算 $G(\mathcal{O}_K)$ 及其 Iwahori 子群的上同调代数，其系数在 $K$ 的剩余域中。 我们的方法涉及对 Lazard 饱和 $p$ 值群理论中出现的一些分次李代数进行新的表示，并将其约化为正特征旗簇的相干上同调。 我们还考虑那些内形的$\mathrm{GL}_n(K)$，它们在稳定同伦理论中导致莫拉稳定子群。 显示英文摘要

摘要： Let $G$ be a split connected reductive group over the ring of integers of a finite unramified extension $K$ of $\mathbf{Q}_p$. Under a standard assumption on the Coxeter number of $G$, we compute the cohomology algebra of $G(\mathcal{O}_K)$ and its Iwahori subgroups, with coefficients in the residue field of $K$. Our methods involve a new presentation of some graded Lie algebras appearing in Lazard's theory of saturated $p$-valued groups, and a reduction to coherent cohomology of the flag variety in positive characteristic. We also consider the case of those inner forms of $\mathrm{GL}_n(K)$ that give rise to the Morava stabilizer groups in stable homotopy theory.