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Bruhat–Tits Theory: A New Approach: New Mathematical Monographs, cartea 44

Autor Tasho Kaletha, Gopal Prasad
en Limba Engleză Hardback – 25 ian 2023
Bruhat–Tits theory is an important topic in number theory, representation theory, harmonic analysis, and algebraic geometry. This book gives the first comprehensive treatment of this theory over 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 gives a review of the relevant background material, touching upon Lie theory, metric geometry, algebraic groups, and integral models. Part II gives a complete, detailed, and motivated treatment of the core theory as well as an axiomatic summary of Bruhat–Tits theory that suffices for the main applications. Part III treats modern topics that have become important in current research. Part IV provides a few sample applications of the theory. The appendices contain further details on the topic of integral models, including a detailed study of integral models.
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Specificații

ISBN-13: 9781108831963
ISBN-10: 1108831966
Pagini: 700
Ilustrații: Worked examples or Exercises; Worked examples or Exercises
Dimensiuni: 158 x 235 x 50 mm
Greutate: 1.26 kg
Ediția:Nouă
Editura: Cambridge University Press
Colecția Cambridge University Press
Seria New Mathematical Monographs

Locul publicării:New York, United States

Cuprins

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.

Notă biografică


Descriere

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