Primes of higher degree and Annihilators of Class groups

2022/09/01 by Mahapatra, Nimish Kumar, Pandey, Prem Prakash, Ram, Mahesh Kumar · 1 citation
#11R29 #11R44 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2209.00328

Abstract

Let L/K be a Galois extension of number fields with Galois group G. We discuss a new method to obtain elements in 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.

Cited by

• Absolutely Abelian Hilbert Class Fields and ℓ-torsion conjecture

Related

• Primes of Higher Degree
• On prime factors of class number of cyclotomic fields
• Singular integers and p-class group of cyclotomic fields
• Annihilating class groups in p-elementary extensions
• Annihilators of the ideal class group of a cyclic extension of a global\n function field