The Steinitz Realization Problem

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 p...

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Bibliographic Details
Published inarXiv.org
Main Author Vemulapalli, Sameera
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 22.06.2024
Subjects
Mathematics - Number Theory
Number theory
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Summary: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 \(K\).
ISSN:2331-8422
DOI:10.48550/arxiv.2406.08643