On number fields with $k$-free discriminants

Joachim König

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arXiv · 1809.01861

On number fields with $k$-free discriminants

Joachim König

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Abstract

Given a finite transitive permutation group $G$, we investigate number fields $F/\mathbb{Q}$ of Galois group $G$ whose discriminant is only divisible by small prime powers. This generalizes previous investigations of number fields with squarefree discriminant. In particular, we obtain a comprehensive result on number fields with cubefree discriminant. Our main tools are arithmetic-geometric, involving in particular an effective criterion on ramification in specializations of Galois covers.

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Joachim König. 2018-09-06. On number fields with $k$-free discriminants. https://arxiv.org/abs/1809.01861

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