Pseudo-reductive groups:
Pseudo-reductive groups arise naturally in the study of general smooth linear algebraic groups over non-perfect fields and have many important applications. This self-contained monograph provides a comprehensive treatment of the theory of pseudo-reductive groups and gives their classification in a u...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2010
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| Schriftenreihe: | New mathematical monographs
17 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | Pseudo-reductive groups arise naturally in the study of general smooth linear algebraic groups over non-perfect fields and have many important applications. This self-contained monograph provides a comprehensive treatment of the theory of pseudo-reductive groups and gives their classification in a usable form. The authors present numerous new results and also give a complete exposition of Tits' structure theory of unipotent groups. They prove the conjugacy results (conjugacy of maximal split tori, minimal pseudo-parabolic subgroups, maximal split unipotent subgroups) announced by Armand Borel and Jacques Tits, and also give the Bruhat decomposition, of general smooth connected algebraic groups. Researchers and graduate students working in any related area, such as algebraic geometry, algebraic group theory, or number theory, will value this book as it develops tools likely to be used in tackling other problems |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xx, 533 pages) |
| ISBN: | 9780511661143 |
| DOI: | 10.1017/CBO9780511661143 |
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| 245 | 1 | 0 | |a Pseudo-reductive groups |c Brian Conrad, Ofer Gabber, Gopal Prasad |
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| 505 | 8 | |a Constructions, examples, and structure theory. Overview of pseudo-reductivity ; Root groups and root systems ; Basic structure theory -- Standard presentations and their applications. Variation of (G', k'/k, T', C) ; Ubiquity of the standard construction ; Classification results -- General classification and applications. The exotic constructions ; Preparations for classification in characteristics 2 and 3 ; The absolutely pseudo-simple groups in characteristic 2 ; General case ; Applications -- Appendices. Background in linear algebraic groups ; Tits' work on unipotent groups in nonzero characteristic ; Rational conjugacy in connected groups | |
| 520 | |a Pseudo-reductive groups arise naturally in the study of general smooth linear algebraic groups over non-perfect fields and have many important applications. This self-contained monograph provides a comprehensive treatment of the theory of pseudo-reductive groups and gives their classification in a usable form. The authors present numerous new results and also give a complete exposition of Tits' structure theory of unipotent groups. They prove the conjugacy results (conjugacy of maximal split tori, minimal pseudo-parabolic subgroups, maximal split unipotent subgroups) announced by Armand Borel and Jacques Tits, and also give the Bruhat decomposition, of general smooth connected algebraic groups. Researchers and graduate students working in any related area, such as algebraic geometry, algebraic group theory, or number theory, will value this book as it develops tools likely to be used in tackling other problems | ||
| 650 | 4 | |a Linear algebraic groups | |
| 650 | 4 | |a Group theory | |
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| 700 | 1 | |a Prasad, Gopal |e Sonstige |4 oth | |
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Datensatz im Suchindex
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|---|---|
| any_adam_object | |
| author | Conrad, Brian 1970- |
| author_facet | Conrad, Brian 1970- |
| author_role | aut |
| author_sort | Conrad, Brian 1970- |
| author_variant | b c bc |
| building | Verbundindex |
| bvnumber | BV043942249 |
| classification_rvk | SK 260 |
| collection | ZDB-20-CBO |
| contents | Constructions, examples, and structure theory. Overview of pseudo-reductivity ; Root groups and root systems ; Basic structure theory -- Standard presentations and their applications. Variation of (G', k'/k, T', C) ; Ubiquity of the standard construction ; Classification results -- General classification and applications. The exotic constructions ; Preparations for classification in characteristics 2 and 3 ; The absolutely pseudo-simple groups in characteristic 2 ; General case ; Applications -- Appendices. Background in linear algebraic groups ; Tits' work on unipotent groups in nonzero characteristic ; Rational conjugacy in connected groups |
| ctrlnum | (ZDB-20-CBO)CR9780511661143 (OCoLC)992929716 (DE-599)BVBBV043942249 |
| dewey-full | 512/.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.55 |
| dewey-search | 512/.55 |
| dewey-sort | 3512 255 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511661143 |
| format | Electronic eBook |
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| id | DE-604.BV043942249 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:17Z |
| institution | BVB |
| isbn | 9780511661143 |
| language | English |
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| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (xx, 533 pages) |
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| publishDate | 2010 |
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| publisher | Cambridge University Press |
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| series2 | New mathematical monographs |
| spelling | Conrad, Brian 1970- Verfasser aut Pseudo-reductive groups Brian Conrad, Ofer Gabber, Gopal Prasad Cambridge Cambridge University Press 2010 1 online resource (xx, 533 pages) txt rdacontent c rdamedia cr rdacarrier New mathematical monographs 17 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Constructions, examples, and structure theory. Overview of pseudo-reductivity ; Root groups and root systems ; Basic structure theory -- Standard presentations and their applications. Variation of (G', k'/k, T', C) ; Ubiquity of the standard construction ; Classification results -- General classification and applications. The exotic constructions ; Preparations for classification in characteristics 2 and 3 ; The absolutely pseudo-simple groups in characteristic 2 ; General case ; Applications -- Appendices. Background in linear algebraic groups ; Tits' work on unipotent groups in nonzero characteristic ; Rational conjugacy in connected groups Pseudo-reductive groups arise naturally in the study of general smooth linear algebraic groups over non-perfect fields and have many important applications. This self-contained monograph provides a comprehensive treatment of the theory of pseudo-reductive groups and gives their classification in a usable form. The authors present numerous new results and also give a complete exposition of Tits' structure theory of unipotent groups. They prove the conjugacy results (conjugacy of maximal split tori, minimal pseudo-parabolic subgroups, maximal split unipotent subgroups) announced by Armand Borel and Jacques Tits, and also give the Bruhat decomposition, of general smooth connected algebraic groups. Researchers and graduate students working in any related area, such as algebraic geometry, algebraic group theory, or number theory, will value this book as it develops tools likely to be used in tackling other problems Linear algebraic groups Group theory Reduktive Gruppe (DE-588)4177313-5 gnd rswk-swf Lineare algebraische Gruppe (DE-588)4295326-1 gnd rswk-swf Reduktive Gruppe (DE-588)4177313-5 s Lineare algebraische Gruppe (DE-588)4295326-1 s 1\p DE-604 Gabber, Ofer 1958- Sonstige oth Prasad, Gopal Sonstige oth Erscheint auch als Druckausgabe 978-0-521-19560-7 https://doi.org/10.1017/CBO9780511661143 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Conrad, Brian 1970- Pseudo-reductive groups Constructions, examples, and structure theory. Overview of pseudo-reductivity ; Root groups and root systems ; Basic structure theory -- Standard presentations and their applications. Variation of (G', k'/k, T', C) ; Ubiquity of the standard construction ; Classification results -- General classification and applications. The exotic constructions ; Preparations for classification in characteristics 2 and 3 ; The absolutely pseudo-simple groups in characteristic 2 ; General case ; Applications -- Appendices. Background in linear algebraic groups ; Tits' work on unipotent groups in nonzero characteristic ; Rational conjugacy in connected groups Linear algebraic groups Group theory Reduktive Gruppe (DE-588)4177313-5 gnd Lineare algebraische Gruppe (DE-588)4295326-1 gnd |
| subject_GND | (DE-588)4177313-5 (DE-588)4295326-1 |
| title | Pseudo-reductive groups |
| title_auth | Pseudo-reductive groups |
| title_exact_search | Pseudo-reductive groups |
| title_full | Pseudo-reductive groups Brian Conrad, Ofer Gabber, Gopal Prasad |
| title_fullStr | Pseudo-reductive groups Brian Conrad, Ofer Gabber, Gopal Prasad |
| title_full_unstemmed | Pseudo-reductive groups Brian Conrad, Ofer Gabber, Gopal Prasad |
| title_short | Pseudo-reductive groups |
| title_sort | pseudo reductive groups |
| topic | Linear algebraic groups Group theory Reduktive Gruppe (DE-588)4177313-5 gnd Lineare algebraische Gruppe (DE-588)4295326-1 gnd |
| topic_facet | Linear algebraic groups Group theory Reduktive Gruppe Lineare algebraische Gruppe |
| url | https://doi.org/10.1017/CBO9780511661143 |
| work_keys_str_mv | AT conradbrian pseudoreductivegroups AT gabberofer pseudoreductivegroups AT prasadgopal pseudoreductivegroups |