This is the first book in English on Bruhatà â â Tits theory, an important topic in number theory, representation theory, and algebraic geometry. A comprehensive account of the theory, it can serve both as a reference for researchers in the field and as a thorough introduction for graduate students and early career mathematicians.
This is the first book in English on Bruhatà â â Tits theory, an important topic in number theory, representation theory, and algebraic geometry. A comprehensive account of the theory, it can serve both as a reference for researchers in the field and as a thorough introduction for graduate students and early career mathematicians.
Tasho Kaletha is Professor of Mathematics at the University of Michigan. He is an expert on the Langlands program, and has studied arithmetic and representation-theoretic aspects of the local Langlands correspondence for p-adic groups.
Inhaltsangabe
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.
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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