Pulling back torsion line bundles to ideal classes

TL;DR

This paper introduces a new technique for constructing and counting number fields with large class groups by studying the specialization of torsion line bundles on varieties over ield.

Contribution

It establishes results linking torsion line bundles on varieties over ields to ideal classes, providing a novel approach to analyze class groups of number fields.

Findings

New method for constructing number fields with large class groups

Results connecting torsion line bundles to ideal class groups

Technique applicable to varieties over ields

Abstract

We prove results concerning the specialisation of torsion line bundles on a variety $V$ defined over $\mathbb{Q}$ to ideal classes of number fields. This gives a new general technique for constructing and counting number fields with large class group.