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 monograph provides a comprehensive treatment of the theory of pseudo-reductive groups and gives their classification in a usable form. In...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2015
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| Ausgabe: | Second edition |
| Schriftenreihe: | New mathematical monographs
26 |
| 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 monograph provides a comprehensive treatment of the theory of pseudo-reductive groups and gives their classification in a usable form. In this second edition there is new material on relative root systems and Tits systems for general smooth affine groups, including the extension to quasi-reductive groups of famous simplicity results of Tits in the semisimple case. Chapter 9 has been completely rewritten to describe and classify pseudo-split absolutely pseudo-simple groups with a non-reduced root system over arbitrary fields of characteristic 2 via the useful new notion of 'minimal type' for pseudo-reductive groups. Researchers and graduate students working in related areas, 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 (xxiv, 665 pages) |
| ISBN: | 9781316092439 |
| DOI: | 10.1017/CBO9781316092439 |
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| 505 | 8 | |a Introduction -- Terminology, conventions, and notation -- Part I: Constructions, Examples, and Structure Theory. 1. Overview of pseudo-reductivity ; 2. Root groups and root systems ; 3. Basic structure theory -- Part II: Standard Presentations and Their Applications. 4. Variation of (G', k'/k, T', C) ; 5. Ubiquity of the standard construction ; 6. Classification results -- Part III: General Classification and Applications. 7. The exotic constructions ; 8. Preparations for classification in characteristics 2 and 3 ; 9. Absolutely pseudo-simple groups in characteristic 2 ; 10. General case ; 11. Applications -- Part IV: Appendices. A. Background in linear algebraic groups ; B. Tits' work on unipotent groups in nonzero characteristic ; C. Rational conjugacy in connected groups -- References -- Index | |
| 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 monograph provides a comprehensive treatment of the theory of pseudo-reductive groups and gives their classification in a usable form. In this second edition there is new material on relative root systems and Tits systems for general smooth affine groups, including the extension to quasi-reductive groups of famous simplicity results of Tits in the semisimple case. Chapter 9 has been completely rewritten to describe and classify pseudo-split absolutely pseudo-simple groups with a non-reduced root system over arbitrary fields of characteristic 2 via the useful new notion of 'minimal type' for pseudo-reductive groups. Researchers and graduate students working in related areas, 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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Datensatz im Suchindex
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| 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 | BV043940202 |
| classification_rvk | SK 260 |
| collection | ZDB-20-CBO |
| contents | Introduction -- Terminology, conventions, and notation -- Part I: Constructions, Examples, and Structure Theory. 1. Overview of pseudo-reductivity ; 2. Root groups and root systems ; 3. Basic structure theory -- Part II: Standard Presentations and Their Applications. 4. Variation of (G', k'/k, T', C) ; 5. Ubiquity of the standard construction ; 6. Classification results -- Part III: General Classification and Applications. 7. The exotic constructions ; 8. Preparations for classification in characteristics 2 and 3 ; 9. Absolutely pseudo-simple groups in characteristic 2 ; 10. General case ; 11. Applications -- Part IV: Appendices. A. Background in linear algebraic groups ; B. Tits' work on unipotent groups in nonzero characteristic ; C. Rational conjugacy in connected groups -- References -- Index |
| ctrlnum | (ZDB-20-CBO)CR9781316092439 (OCoLC)910524527 (DE-599)BVBBV043940202 |
| 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/CBO9781316092439 |
| edition | Second edition |
| format | Electronic eBook |
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| id | DE-604.BV043940202 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:13Z |
| institution | BVB |
| isbn | 9781316092439 |
| language | English |
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| physical | 1 online resource (xxiv, 665 pages) |
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| publishDate | 2015 |
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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, Stanford University, Ofer Gabber, Institut des hautes études scientifiques, Gopal Prasad, University of Michigan Second edition Cambridge Cambridge University Press 2015 1 online resource (xxiv, 665 pages) txt rdacontent c rdamedia cr rdacarrier New mathematical monographs 26 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Introduction -- Terminology, conventions, and notation -- Part I: Constructions, Examples, and Structure Theory. 1. Overview of pseudo-reductivity ; 2. Root groups and root systems ; 3. Basic structure theory -- Part II: Standard Presentations and Their Applications. 4. Variation of (G', k'/k, T', C) ; 5. Ubiquity of the standard construction ; 6. Classification results -- Part III: General Classification and Applications. 7. The exotic constructions ; 8. Preparations for classification in characteristics 2 and 3 ; 9. Absolutely pseudo-simple groups in characteristic 2 ; 10. General case ; 11. Applications -- Part IV: Appendices. A. Background in linear algebraic groups ; B. Tits' work on unipotent groups in nonzero characteristic ; C. Rational conjugacy in connected groups -- References -- Index Pseudo-reductive groups arise naturally in the study of general smooth linear algebraic groups over non-perfect fields and have many important applications. This monograph provides a comprehensive treatment of the theory of pseudo-reductive groups and gives their classification in a usable form. In this second edition there is new material on relative root systems and Tits systems for general smooth affine groups, including the extension to quasi-reductive groups of famous simplicity results of Tits in the semisimple case. Chapter 9 has been completely rewritten to describe and classify pseudo-split absolutely pseudo-simple groups with a non-reduced root system over arbitrary fields of characteristic 2 via the useful new notion of 'minimal type' for pseudo-reductive groups. Researchers and graduate students working in related areas, 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 Lineare algebraische Gruppe (DE-588)4295326-1 gnd rswk-swf Reduktive Gruppe (DE-588)4177313-5 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 978-1-107-08723-1 https://doi.org/10.1017/CBO9781316092439 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 Introduction -- Terminology, conventions, and notation -- Part I: Constructions, Examples, and Structure Theory. 1. Overview of pseudo-reductivity ; 2. Root groups and root systems ; 3. Basic structure theory -- Part II: Standard Presentations and Their Applications. 4. Variation of (G', k'/k, T', C) ; 5. Ubiquity of the standard construction ; 6. Classification results -- Part III: General Classification and Applications. 7. The exotic constructions ; 8. Preparations for classification in characteristics 2 and 3 ; 9. Absolutely pseudo-simple groups in characteristic 2 ; 10. General case ; 11. Applications -- Part IV: Appendices. A. Background in linear algebraic groups ; B. Tits' work on unipotent groups in nonzero characteristic ; C. Rational conjugacy in connected groups -- References -- Index Linear algebraic groups Group theory Lineare algebraische Gruppe (DE-588)4295326-1 gnd Reduktive Gruppe (DE-588)4177313-5 gnd |
| subject_GND | (DE-588)4295326-1 (DE-588)4177313-5 |
| title | Pseudo-reductive groups |
| title_auth | Pseudo-reductive groups |
| title_exact_search | Pseudo-reductive groups |
| title_full | Pseudo-reductive groups Brian Conrad, Stanford University, Ofer Gabber, Institut des hautes études scientifiques, Gopal Prasad, University of Michigan |
| title_fullStr | Pseudo-reductive groups Brian Conrad, Stanford University, Ofer Gabber, Institut des hautes études scientifiques, Gopal Prasad, University of Michigan |
| title_full_unstemmed | Pseudo-reductive groups Brian Conrad, Stanford University, Ofer Gabber, Institut des hautes études scientifiques, Gopal Prasad, University of Michigan |
| title_short | Pseudo-reductive groups |
| title_sort | pseudo reductive groups |
| topic | Linear algebraic groups Group theory Lineare algebraische Gruppe (DE-588)4295326-1 gnd Reduktive Gruppe (DE-588)4177313-5 gnd |
| topic_facet | Linear algebraic groups Group theory Lineare algebraische Gruppe Reduktive Gruppe |
| url | https://doi.org/10.1017/CBO9781316092439 |
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