# Constructing abelian extensions with prescribed norms

@article{Frei2020ConstructingAE,
title={Constructing abelian extensions with prescribed norms},
author={C. Frei and R. Richard},
journal={arXiv: Number Theory},
year={2020}
}
• Published 2020
• Mathematics
• arXiv: Number Theory
Given a number field $K$, a finite abelian group $G$ and finitely many elements $\alpha_1,\ldots,\alpha_t\in K$, we construct abelian extensions $L/K$ with Galois group $G$ that realise all of the elements $\alpha_1,\ldots,\alpha_t$ as norms of elements in $L$. In particular, this shows existence of such extensions for any given parameters. Our approach relies on class field theory and a recent formulation of Tate's characterisation of the Hasse norm principle, a local-global principle for… Expand

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