Corrigendum: Strong $\mathbb A^1$-invariance of $\mathbb A^1$-connected components of reductive algebraic groups (J. Topol. 16 (2023), no. 2, 634--649.)

TL;DR

This corrigendum provides a complete, self-contained proof of a key lemma in the study of $ ext{A}^1$-invariance of connected components in reductive algebraic groups, addressing gaps in previous proofs.

Contribution

It offers a revised, comprehensive proof of an important lemma, strengthening the original results on $ ext{A}^1$-connected components of reductive algebraic groups.

Findings

Complete proof of Lemma 5.1 provided

Addresses gaps in previous proof by Choudhury-Hagadi

Reinforces $ ext{A}^1$-invariance results for reductive groups

Abstract

The proof of Lemma 5.1 in the paper Strong $\mathbb A^1$-invariance of $\mathbb A^1$-connected components of reductive algebraic groups (J. Topol. 16 (2023), no. 2, 634--649) is incomplete as it relies on some results of Choudhury-Hagadi, the proof of which contains a gap. The goal of this note is to give a complete and self-contained proof of this lemma.