A geometric approach to large class groups: a survey

TL;DR

This survey reviews methods for constructing large class groups of number fields via specialization of finite covers of curves and discusses various applications of these techniques.

Contribution

It compiles and explains existing results and techniques related to large class groups, providing a comprehensive overview of this area.

Findings

Methods for constructing large class groups are effective and versatile.

Specialization of finite covers is a key technique in this construction.

Applications include explicit examples and potential further research directions.

Abstract

The purpose of this note is twofold. First, we survey results on the construction of large class groups of number fields by specialization of finite covers of curves. Then we give examples of applications of these techniques.