Notice bibliographique
- Notice
Type(s) de contenu et mode(s) de consultation : Texte noté : sans médiation
Auteur(s) : Kaletha, Tasho
Prasad, Gopal
Titre(s) : Bruhat-Tits theory [Texte imprimé] : a new approach / Tasho Kaletha,... Gopal Prasad,...
Publication : Cambridge : Cambridge university press, copyright 2023
Description matérielle : 1 vol. (XXX-718 p.) ; 24 cm
Collection : New mathematical monographs ; 44
Lien à la collection : New mathematical monographs
Note(s) : Bibliogr. p. 708-714. Index
"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"
Sujet(s) : Immeubles (théorie des groupes)
Théorie des nombres
Indice(s) Dewey :
512.2 (23e éd.) = Groupes et théorie des groupes (mathématiques)
Identifiants, prix et caractéristiques : ISBN 978-1-108-83196-3 (rel.)
Identifiant de la notice : ark:/12148/cb47278264z
Notice n° :
FRBNF47278264
(notice reprise d'un réservoir extérieur)
Table des matières : 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.
