An introduction to arithmetic groups

Christophe Soule (1)

1 IHES - Institut des Hautes Études Scientifiques

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 indexgiven by congruence conditions? Finally, we shall discuss rigidityproperties of arithmetic groups.

Mots clés: arithmetic groups; reduction theory; presentations; rigidity

Domaines: Théorie des groupes [math.GR]

Christophe Soule. An introduction to arithmetic groups. 2004. ⟨hal-00001348⟩