On homology of linear groups over k[t]

TL;DR

This paper proves that for any simply-connected reductive group G over an infinite field k, the inclusion of k into k[t] induces an isomorphism on homology, extending previous results by Soule and Knudson.

Contribution

It generalizes the homology isomorphism result for linear groups over polynomial rings to all simply-connected reductive groups over infinite fields.

Findings

Inclusion of k into k[t] induces homology isomorphism for G.

Extends previous results to a broader class of groups.

Provides a unified proof for reductive groups over infinite fields.

Abstract

This note explains how to prove that for any simply-connected reductive group G and any infinite field k, the inclusion of k in k[t] induces an isomorphism on homology. This generalizes results of Soule and Knudson.