Book contents
- Frontmatter
- Dedication
- Contents
- Illustrations
- Tables
- Introduction
- Part One Background and Review
- Part Two Bruhat–Tits Theory
- 3 Examples: Quasi-split Simple Groups of Rank 1
- 4 Overview and Summary of Bruhat–Tits Theory
- 5 Bruhat, Cartan, and Iwasawa Decompositions
- 6 The Apartment
- 7 The Bruhat–Tits Building for a Valuation of the Root Datum
- 8 Integral Models
- 9 Unramified Descent
- Part Three Additional Developments
- Part Four Applications
- Part Five Appendices
- References
- Index of Symbols
- General Index
4 - Overview and Summary of Bruhat–Tits Theory
from Part Two - Bruhat–Tits Theory
Published online by Cambridge University Press: 16 May 2023
Book contents
- Frontmatter
- Dedication
- Contents
- Illustrations
- Tables
- Introduction
- Part One Background and Review
- Part Two Bruhat–Tits Theory
- 3 Examples: Quasi-split Simple Groups of Rank 1
- 4 Overview and Summary of Bruhat–Tits Theory
- 5 Bruhat, Cartan, and Iwasawa Decompositions
- 6 The Apartment
- 7 The Bruhat–Tits Building for a Valuation of the Root Datum
- 8 Integral Models
- 9 Unramified Descent
- Part Three Additional Developments
- Part Four Applications
- Part Five Appendices
- References
- Index of Symbols
- General Index
Summary
Contains a summary of Bruhat--Tits theory and closely related material. More precisely, in Section 1 we state most major results of the theory in the form of Axioms. This section can serve as a convenient reference for the expert as well as an initial overview for the beginner before diving into the specifics of the theory. Building on these axioms, in Section 2 we define and study the metric on the Bruhat--Tits building, in Section 3 we define the enlarged building, and in Section 4 we formulate various uniqueness properties of the building.
- Type
- Chapter
- Information
- Bruhat–Tits TheoryA New Approach, pp. 157 - 185Publisher: Cambridge University PressPrint publication year: 2023