A conductor formula for completed group algebras

Abstract

Let $\mathcal{O}$ be the ring of integers in a finite extension of ${\mathbb{Q}}_p$. If $G$ is a finite group and $\Gamma$ is a maximal order containing the group ring $\mathcal{O}[G]$, Jacobinski's conductor formula gives a complete description of the central conductor of $\Gamma$ 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.

23 pages; many improvements and corrections since v1; minor changes since v4

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