Corrigendum \`a "Sous-groupe de Brauer invariant et obstruction de descente it\'er\'ee" Algebra & Number Theory 14 (2020), no. 8, 2151--2183

TL;DR

This corrigendum addresses an error in a previous work regarding a K"unneth formula statement, providing corrections while affirming the validity of the remaining results.

Contribution

The paper corrects a specific mathematical statement about the K"unneth formula in an earlier publication, ensuring the accuracy of the overall results.

Findings

Correction of the K"unneth formula statement

Validation of the remaining results in the original paper

Clarification of the impact of the corrigendum

Abstract

The \S 2 of our work "Sous-groupe de Brauer invariant et obstruction de descente it\'er\'ee" uses a statement about the degree two K\"unneth formula proved by Skorobogatov and Zarhin in their paper "The Brauer group and the Brauer-Manin set of products of varieties". Recently they find that this statement is not correct (see their Corrigendum). We correct \S 2 of our paper. The rest of our paper is still correct.