Bruhat-Tits theory: a new approach
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...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2023
|
| Schriftenreihe: | New mathematical monographs
44 |
| Schlagworte: | |
| Online-Zugang: | BSB01 BTU01 FHN01 UBG01 Volltext |
| Zusammenfassung: | 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 |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 16 May 2023) 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 |
| Beschreibung: | 1 Online-Ressource (xxx, 718 Seiten) |
| ISBN: | 9781108933049 |
| DOI: | 10.1017/9781108933049 |
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| spelling | Kaletha, Tasho aut Bruhat-Tits theory a new approach Tasho Kaletha, Gopal Prasad Cambridge Cambridge University Press 2023 1 Online-Ressource (xxx, 718 Seiten) txt rdacontent c rdamedia cr rdacarrier New mathematical monographs 44 Title from publisher's bibliographic system (viewed on 16 May 2023) 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 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 Buildings (Group theory) Number theory Prasad, Gopal 1945- (DE-588)136265367 aut Erscheint auch als Druck-Ausgabe 978-1-108-83196-3 https://doi.org/10.1017/9781108933049 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Kaletha, Tasho Prasad, Gopal 1945- Bruhat-Tits theory a new approach Buildings (Group theory) Number theory |
| title | Bruhat-Tits theory a new approach |
| title_auth | Bruhat-Tits theory a new approach |
| title_exact_search | Bruhat-Tits theory a new approach |
| title_exact_search_txtP | Bruhat-Tits theory a new approach |
| title_full | Bruhat-Tits theory a new approach Tasho Kaletha, Gopal Prasad |
| title_fullStr | Bruhat-Tits theory a new approach Tasho Kaletha, Gopal Prasad |
| title_full_unstemmed | Bruhat-Tits theory a new approach Tasho Kaletha, Gopal Prasad |
| title_short | Bruhat-Tits theory |
| title_sort | bruhat tits theory a new approach |
| title_sub | a new approach |
| topic | Buildings (Group theory) Number theory |
| topic_facet | Buildings (Group theory) Number theory |
| url | https://doi.org/10.1017/9781108933049 |
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