Dedication

pp v-vi

Contents

pp vii-xi

Illustrations

pp xii-xii

Tables

pp xiii-xiv

Introduction

pp xv-xxx

Part One - Background and Review

pp 1-2

1 - Affine Root Systems and Abstract Buildings

pp 3-67

2 - Algebraic Groups

pp 68-138

Part Two - Bruhat–Tits Theory

pp 139-140

3 - Examples: Quasi-split Simple Groups of Rank 1

pp 141-156

4 - Overview and Summary of Bruhat–Tits Theory

pp 157-185

5 - Bruhat, Cartan, and Iwasawa Decompositions

pp 186-194

6 - The Apartment

pp 195-234

7 - The Bruhat–Tits Building for a Valuation of the Root Datum

pp 235-282

8 - Integral Models

pp 283-322

9 - Unramified Descent

pp 323-386

Part Three - Additional Developments

pp 387-388

10 - Residue Field of Dimension 1

pp 389-419

11 - Component Groups of Integral Models

pp 420-435

12 - Finite Group Actions and Tamely Ramified Descent

pp 436-465

13 - Moy–Prasad Filtrations

pp 466-489

14 - Functorial Properties

pp 490-512

15 - The Buildings of Classical Groups via Lattice Chains

pp 513-544

Part Four - Applications

pp 545-546

16 - Classification of Maximal Unramified Tori (d’aprés DeBacker)

pp 547-552

17 - Classification of Tamely Ramified Maximal Tori

pp 553-557

18 - The Volume Formula

pp 558-590

Part Five - Appendices

pp 591-592

A - Operations on Integral Models

pp 593-652