Bruhat-Tits theory : A new approach /
Tasho Kaletha, Gopal Prasad.
- xxx, 718 pages : illustrations.
- New mathematical monographs ; 44. .
- New mathematical monographs ; 44. .
Includes bibliographical references and indexes.
Affine root systems and abstract buildings -- Algebraic groups -- Examples: quasi-split simple groups of rank 1 -- Overview and summary of Bruhat-Tits theory -- The Apartment -- The Bruhat-Tits building for a valuation of the root datum -- Integral models -- Unramified descent -- Residue field F of dimension <1 -- Component groups of integral models -- Finite group actions and tamely ramified descent -- Moy-Prasad filtrations -- Functorial properties -- The buildings of classical groups via Lattice chains -- Classification of maximal unramified tori (dʼaprès DeBacker) -- Classification of tamely ramified maximal tori -- The volume formula.
"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. 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 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 the integral models of tori"--