Reductive groups and Steinberg maps

TL;DR

This paper introduces foundational concepts of reductive algebraic groups over finite fields, aiming to develop the character theory of finite groups of Lie type.

Contribution

It provides the initial foundational framework for understanding reductive groups over finite fields, essential for studying their character theory.

Findings

Establishment of basic properties of reductive algebraic groups

Framework for character theory of finite groups of Lie type

Preliminary groundwork for a comprehensive book on the subject

Abstract

This is a preliminary version of the first chapter of a book project on the character theory of finite groups of Lie type. It provides the foundations from the general theory of reductive algebraic groups over a finite field.