Bruhat–Tits Theory

图书简介

The theory of Bruhat–Tits buildings is an important topic in number theory, representation theory, and algebraic geometry. This book, the first in English on the subject, gives a comprehensive account of Bruhat–Tits theory for discretely valued Henselian fields. It can serve both as a reference for researchers in the field and as a thorough introduction for graduate students and early career mathematicians. Part I of the book begins with a review of relevant background material before proceeding to give a complete, detailed, and motivated treatment of the core theory. For more experienced readers looking to learn the essentials for use in their own work, there is also an axiomatic summary of Bruhat–Tits theory that suffices for the main applications. Part II treats modern topics that have become important at the cutting edge of research, while the appendices contain further details on more specialized background material.

Introduction; Part I. Background and Review: 1. Affine root systems and abstract buildings; 2. Algebraic groups; Part II. Bruhat–Tits Theory: 3. Examples: Quasi-split 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 III. Additional Developments: 10. Residue field f of dimension ≤ 1; 11. The buildings of classical groups via lattice chains; 12. Component groups of integral models; 13. Finite group actions and tamely ramified descent; 14. Moy–Prasad filtrations; 15. Functorial properties; Part IV. Applications: 16. Classification of maximal unramified tori (d’après DeBacker); 17. Classification of tamely ramified maximal tori; 18. The volume formula; Part V. Appendices: A. Operations on integral models; B. Integral models of tori; C. Integral models of root subgroups; References; Index.

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Bruhat–Tits Theory（New Mathematical Monographs, 44） Bruhat-Tits 理论：一种新方法 数论

Bruhat–Tits Theory（New Mathematical Monographs, 44）

Bruhat-Tits 理论：一种新方法
数论