完备群代数的导子公式
A conductor formula for completed group algebras
摘要：
设$\mathcal O$是$\mathbb Q_p$的有限扩张中的整数环.若$G$是有限群，$Γ$是包含群环$\mathcal O[G]$的极大阶，Jacobinski的导子公式根据$G$的特征标给出了$Γ$的中心导子到$\mathcal O[G]$的完整刻画.对于完全群代数代数$\mathcal O[[G]]$，我们证明了一个类似的结果，其中$G$是维数为$1$的$p$ -adic李群.我们还将讨论这一结果的几个后果。
英文摘要：
Let $\mathcal O$ be the ring of integers in a finite extension of $\mathbb Q_p$. If $G$ is a finite group and $Γ$ is a maximal order containing the group ring $\mathcal O[G]$, Jacobinski's conductor formula gives a complete description of the central conductor of $Γ$ into $\mathcal O[G]$ in terms of characters of $G$. We prove a similar result for completed group algebras $\mathcal O[[G]]$, where $G$ is a $p$-adic Lie group of dimension $1$. We will also discuss several consequences of this result.
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