The 2-Selmer group of $S_n$-number fields of even degree

TL;DR

This paper extends existing models to analyze the 2-Selmer groups of even-degree $S_n$-number fields, providing new heuristics on the relationship between class group and narrow class group ranks.

Contribution

It introduces a novel extension of the Dummit and Voight model to even-degree $S_n$-number fields and develops heuristics for 2-rank differences.

Findings

Extended the 2-Selmer group model to even-degree $S_n$-number fields

Proposed heuristics for the difference in 2-ranks between class and narrow class groups

Provided insights into the structure of 2-Selmer groups in new number field families

Abstract

This paper is an extension of the work of Dummit and Voight on modeling the 2-Selmer group of number fields. We extend their model to $S_n$-number fields of even degree and develop heuristics on the difference in the 2-ranks between the class group and narrow class group.