Book contents
- Frontmatter
- Contents
- Preface to the Second English Edition
- Preface to the First English Edition (1994)
- Preface to the Russian Edition (1991)
- List of Notations
- 1 Algebraic Number Theory
- 2 Algebraic Groups
- 3 Algebraic Groups over Locally Compact Fields
- 4 Arithmetic Groups and Reduction Theory
- 5 Adeles
- Bibliography
- Index
2 - Algebraic Groups
Published online by Cambridge University Press: 17 August 2023
Book contents
- Frontmatter
- Contents
- Preface to the Second English Edition
- Preface to the First English Edition (1994)
- Preface to the Russian Edition (1991)
- List of Notations
- 1 Algebraic Number Theory
- 2 Algebraic Groups
- 3 Algebraic Groups over Locally Compact Fields
- 4 Arithmetic Groups and Reduction Theory
- 5 Adeles
- Bibliography
- Index
Summary
This chapter assembles the material from the theory of linear algebraic groups that is used routinely in the remainder of the book. The first section summarizes the basic structure theory, including the classification of semisimple groups over algebraically closed fields. The second section discusses the classification of forms in terms of Galois cohomology, which is then applied in the third section to give a description of the classical groups. The fourth section contains miscellaneous results from algebraic geometry.
- Type
- Chapter
- Information
- Algebraic Groups and Number Theory , pp. 53 - 123Publisher: Cambridge University PressPrint publication year: 2023