Bruhat-Tits theory : a new approach / Tasho Kaletha, Gopal Prasad.

Format:

Book

Author/Creator:

Kaletha, Tasho, author.

Prasad, Gopal, author.

Series:

New mathematical monographs ; 44.

New mathematical monographs ; 44

Language:

English

Subjects (All):

Buildings (Group theory).

Number theory.

Physical Description:

1 online resource (xxx, 718 pages) : digital, PDF file(s).

Place of Publication:

Cambridge ; New York : Cambridge University Press, 2023.

Summary:

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.

Contents:

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.

Notes:

Title from publisher's bibliographic system (viewed on 16 May 2023).

Other Format:

Print version:

ISBN:

9781108933049 (ebook)

Access Restriction:

Restricted for use by site license.