Primes of higher degree and Annihilators of Class groups

TL;DR

This paper introduces a novel method to find elements in group rings that annihilate class groups of number fields, especially cyclotomic fields, emphasizing the significance of primes with higher residue degrees.

Contribution

It presents a new approach to constructing annihilators of class groups in Galois extensions, with specific applications to cyclotomic fields and primes of higher residue degree.

Findings

New annihilators for class groups of cyclotomic fields

Connections between primes of higher residue degree and class group structure

Implications for number theory and algebraic number fields

Abstract

Let $L/K$ be a Galois extension of number fields with Galois group $G$. We discuss a new method to obtain elements in $\mathbb{Z}[G]$ which annihilate the class group of $L$. Using this method, we obtain annihilators of class groups of cyclotomic fields. We show that these annihilators are new. Some more consequences are also discussed. Moreover, we mention some results and connections to highlight importance of primes of higher residue degree.