Bruhat-Tits Theory: A New Approach

ISBN-13: 9781108831963 / Angielski / Twarda / 2023 / 700 str.

Ann Arbor) Prasad Gopal (University of Michigan

Opis

Comprehensive treatment of Bruhat–Tits theory for graduate students and researchers in number theory, representation theory, and algebraic geometry.

Spis treści

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.