Fr. 50.90

Finiteness Properties of Arithmetic Groups Acting on Twin Buildings

English · Paperback / Softback

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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

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