The structure of the group G(k[t]): Variations on a theme of Soulé

Margaux, Benedictus

doi:10.2140/ant.2009.3.393

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The structure of the group {\slshape\bfseries G}(\kern-.1emk\/[t\kern.1em]): Variations on a theme of Soulé

Benedictus Margaux

Vol. 3 (2009), No. 4, 393–409

DOI: 10.2140/ant.2009.3.393

Abstract

Following Soulé’s ideas from 1979, we give a presentation of the abstract group $G (k [t])$ for any semisimple (connected) simply connected absolutely almost simple $k$ -group $G (k [t])$ . As an application, we give a description of $G (k [t])$ in terms of direct limits, and show that the Whitehead group and the naive group of connected components of $G (k [t])$ coincide.

Keywords

Bruhat–Tits buildings, arithmetic groups, simplicial fundamental domain

Mathematical Subject Classification 2000

Primary: 20G10

Secondary: 20F05

Milestones

Received: 19 November 2007

Revised: 5 November 2008

Accepted: 11 November 2008

Published: 15 June 2009

Authors

Benedictus Margaux

Vol. 3, No. 4, 2009