Restricting the splitting types of a positive density set of places in number field extensions

Alberts, Brandon

doi:10.1090/proc/16687

Restricting the splitting types of a positive density set of places in number field extensions
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by Brandon Alberts;

Proc. Amer. Math. Soc. 152 (2024), 1907-1914

DOI: https://doi.org/10.1090/proc/16687

Published electronically: March 20, 2024

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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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