A conductor formula for completed group algebras

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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