Ideal class groups of cyclotomic number fields III

TL;DR

This paper explores the construction of unramified abelian extensions of cyclotomic number fields, building on Scholz's idea, to advance understanding of their ideal class groups.

Contribution

It introduces a novel method for constructing unramified abelian extensions of cyclotomic fields based on Scholz's idea.

Findings

New constructions of unramified abelian extensions

Deeper insights into ideal class groups of cyclotomic fields

Extension of Scholz's classical ideas

Abstract

Using an idea going back to Scholz, we construct unramified abelian extensions of cyclotomic extensions of number fields.