On unit signatures and narrow class groups of odd degree abelian number fields

TL;DR

This paper investigates the structure of 2-Selmer groups, unit signature ranks, and narrow class groups in odd degree abelian number fields, providing theoretical results and distribution predictions.

Contribution

It offers new structural insights and distribution predictions for unit signatures and narrow class groups in fixed-degree, fixed-Galois group abelian number fields.

Findings

Structural results on 2-Selmer groups as Galois modules

Predictions for distribution of unit signature ranks

Analysis of narrow class groups in specific families

Abstract

For an abelian number field of odd degree, we study the structure of its 2-Selmer group as a bilinear space and as a Galois module. We prove structural results and make predictions for the distribution of unit signature ranks and narrow class groups in families where the degree and Galois group are fixed.