On arithmetic subgroups of simple algebraic groups

Algebraic Groups, Lie Groups, and their Arithmetic Subgroups

This work is a modern exposition of the theory of algebraic group schemes, Lie groups, and their arithmetic subgroups. It supersedes Algebraic Groups and Arithmetic Groups. This file only contains the front matter. For the rest, see Single paper copies for noncommercial personal use may be made without explicit permission from the copyright holder. Preface For one who attempts to unravel the st...

Some good-filtration subgroups of simple algebraic groups

Let G be a connected and reductive algebraic group over an algebraically closed field of characteristic p > 0. An interesting class of representations of G consists of those G-modules having a good filtration – i.e. a filtration whose layers are the induced highest weight modules obtained as the space of global sections of G-linearized line bundles on the flag variety of G. Let H ⊂ G be a conne...

Algebraic Groups and Arithmetic Groups

Finite Subgroups of Algebraic Groups

0. Introduction 1105 1. Constructible families 1111 2. Genericity for finite subgroups 1116 3. Finite groups of Lie type 1119 4. Basic nonconcentration estimate 1122 5. Finite subgroups of abelian varieties 1126 6. Orders of conjugacy classes and centralizers 1127 7. Regular semisimple and unipotent elements 1129 8. Minimal unipotent elements 1134 9. Frobenius map 1140 10. Traces in the basic c...

Constructing Arithmetic Subgroups of Unipotent Groups

Let G be a unipotent algebraic subgroup of some GLm(C) defined over Q. We describe an algorithm for finding a finite set of generators of the subgroup G(Z) = G ∩ GLm(Z). This is based on a new proof of the result (in more general form due to Borel and Harish-Chandra) that such a finite generating set exists.