On presentations of integer polynomial points of simple groups over number fields

TL;DR

This paper investigates the algebraic structure of integer polynomial points of simple algebraic groups over number fields, showing that certain groups are not finitely presented when the K-rank is 2.

Contribution

It establishes a new non-finite presentation result for integer polynomial points of simple algebraic groups over number fields when the K-rank equals 2.

Findings

G(A[t]) is not finitely presented for K-rank 2 groups

Provides insights into the algebraic structure of polynomial points over number fields

Advances understanding of the finiteness properties of algebraic groups over rings

Abstract

Let K be a number field and let A be its ring of integers. Let G be a connected, noncommutative, absolutely almost simple algebraic K-group. If the K-rank of G equals 2, then G(A[t]) is not finitely presented.