An introduction to arithmetic groups

2004/03/23 by Christophe Soule, Soule, Christophe
Mathematics · #20G30 #20G35 #20G45 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20G30 #msc:20G35 #msc:20G45

paper · pdf · doi:10.48550/arxiv.math/0403390

Talks at the Conference ``Frontiers in Number Theory, Physics and Geometry'', Les Houches, March 9-21, 2003

arxiv created 2004/03/23 · arxiv updated 2009/12/01

Abstract

Arithmetic groups are groups of matrices with integral entries. We shall first discuss their origin in number theory (Gauss, Minkowski) and their role in the "reduction theory of quadratic forms". Then we shall describe these groups by generators and relations. The next topic will be: are all subgroups of finite index given by congruence conditions? Finally, we shall discuss rigidity properties of arithmetic groups.

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