SL(n,Z[t]) is not FP_{n-1}

TL;DR

This paper demonstrates that the group SL(n,Z[t]) does not have the property FP_{n-1} by employing geometric methods involving Euclidean buildings.

Contribution

It introduces a novel geometric approach to analyze algebraic properties of SL(n,Z[t]) using Euclidean buildings.

Findings

SL(n,Z[t]) is not FP_{n-1}

Utilizes Euclidean building geometry in algebraic group analysis

Provides new insights into the finiteness properties of algebraic groups

Abstract

We prove the result from the title using the geometry of Euclidean buildings.