The Hasse norm principle for abelian extensions -- corrigendum

TL;DR

This corrigendum corrects errors in the proofs of key theorems related to the Hasse norm principle for abelian extensions, reaffirming the validity of the original results with proper proofs.

Contribution

The paper provides corrected proofs for the main theorems in the original work on the Hasse norm principle for abelian extensions.

Findings

Corrected proofs of Theorem 1.1 and Theorem 1.5(2)

Validation of the original results with new proofs

Clarification of the techniques used in the original paper

Abstract

The proofs of Theorem 1.1 and Theorem 1.5(2) in the authors' paper 'The Hasse norm principle for abelian extensions' are incorrect. We point out the mistakes and provide correct proofs, using techniques of the original paper.