Construction of a $p$-extension of number fields whose unit group has prescribed Galois module structure

Abstract

Let $G$ be a finite $p$-group. We construct a $G$-extension $K/k$ of number fields such that the $p$-adic completion of the unit group of $K$ has a prescribed ${\mathbb{Z}}_p[G]$-module structure, up to free direct summands.

9 pages