The Steinitz Realization Problem

Abstract

Let $K$ be a number field and let $n\in {\mathbb{Z}}_{>1}$. The Steinitz realization problem asks: does every element of the ideal class group of $K$ occur as the Steinitz class of a degree $n$ extension of $K$? In this article, we give an affirmative answer to the Steinitz realization problem for all $n$ and $K$.

arXiv commentVersion 2. Fixed several minor typo and expanded the proof of Lemma 3.1. 5 pages. Comments welcome!