Finiteness Properties of Arithmetic Groups Acting on Twin Buildings

Providing an accessible approach to a special case of the Rank Theorem, the present text considers the exact finiteness properties of S-arithmetic subgroups of split reductive groups in positive characteristic when S contains only two places. While the proof of the general Rank Theorem uses an involved reduction theory due to Harder, by imposing the restrictions that the group is split and that S has only two places, one can instead make use of the theory of twin buildings.

List of contents

Basic Definitions and Properties.- Finiteness Properties of G(Fq[t]).- Finiteness Properties of G(Fq[t; t^-1]).- Affine Kac-Moody Groups.- Adding Places.

Summary

Providing an accessible approach to a special case of the Rank Theorem, the present text considers the exact finiteness properties of S-arithmetic subgroups of split reductive groups in positive characteristic when S contains only two places. While the proof of the general Rank Theorem uses an involved reduction theory due to Harder, by imposing the restrictions that the group is split and that S has only two places, one can instead make use of the theory of twin buildings.

Product details

• Authors: Stefan Witzel
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 27.03.2014
• EAN: 9783319064765
• ISBN: 978-3-31-906476-5
• No. of pages: 113
• Dimensions: 157 mm x 8 mm x 235 mm
• Weight: 213 g
• Illustrations: XVI, 113 p. 11 illus.
• Series: Lecture Notes in Mathematics; Lecture Notes in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra; B, geometry, Group Theory, Mathematics and Statistics, Manifolds and Cell Complexes (incl. Diff.Topology), Manifolds (Mathematics), Analytic geometry, Manifolds and Cell Complexes, Complex manifolds, Analytic topology, Group Theory and Generalizations, Algebraic Topology