A Conductor Formula for Completed Group Algebras

Let $\fo$ be the ring of integers in a finite extension of $\qp$. If $G$ is a finite group and $\Ga$ is a maximal $\fo$-order containing the group ring $\fo[G]$, Jacobinski's conductor formula gives a complete description of the central conductor of $\Ga$ into $\fo[G]$ in terms of characters of $G$. We prove a similar result for completed group algebras $\fo [[G]]$, where $G$ is a $p$-adic Lie group of dimension 1. We will also discuss several consequences of this result.

2010 Mathematics Subject Classification: 16H10, 16H20, 11R23

Keywords and Phrases: central conductor, completed group algebras, extensions of lattices, Fitting invariants

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