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arXiv · 2309.12525

Restricting the Splitting Types of a Positive Density Set of Places in Number Field Extensions

Brandon Alberts
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Abstract

We prove necessary and sufficient conditions for a finite group $G$ with an ordering of $G$-extensions to satisfy the following property: for every positive density set of places $A$ of a number field $K$ and every splitting type given by a conjugacy class $c$ in $G$, $0\%$ of $G$-extensions avoid this splitting type for each $p\in A$.

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Brandon Alberts. 2023-09-21. Restricting the Splitting Types of a Positive Density Set of Places in Number Field Extensions. https://arxiv.org/abs/2309.12525

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