Classification of pseudo-reductive groups:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Princeton and Oxford
Princeton University Press
2016
|
| Schriftenreihe: | Annals of mathematics studies
Number 191 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028421509&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Literaturverzeichnis Seite 239-240 |
| Umfang: | vii, 245 Seiten |
| ISBN: | 9780691167923 |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text | Titel: Classification of pseudo-reductive groups
Autor: Conrad, Brian
Jahr: 2016
Contents 1 Introduction 1 1.1 Motivation............................ 1 1.2 Root systems and new results.................. 4 1.3 Exotic groups and degenerate quadratic forms......... 5 1.4 Tame central extensions..................... 6 1.5 Generalized standard groups.................. 8 1.6 Minimal type and general structure theorem.......... 10 1.7 Galois-twisted forms and Tits classification.......... 11 1.8 Background, notation, and acknowledgments ......... 13 2 Preliminary notions 15 2.1 Standard groups, Levi subgroups, and root systems...... 15 2.2 The basic exotic construction.................. 19 2.3 Minimal type.......................... 21 3 Field-theoretic and linear-algebraic invariants 28 3.1 A non-standard rank-1 construction .............. 28 3.2 Minimal field of definition for u (Gj) ............ 37 3.3 Root field and applications...................• 41 3.4 Application to classification results............... 50 4 Central extensions and groups locally of minimal type 57 4.1 Central quotients........................ 57 4.2 Beyond the quadratic case ................... 60 4.3 Groups locally of minimal type................. 62 5 Universal smooth k -tame central extension 66 5.1 Construction of central extensions............... 66 5.2 A universal construction .................... 73
CONTENTS vi 5.3 Properties and applications of G ................ 75 6 Automorphisms, isomorphisms, and Tits classification 79 6.1 Isomorphism Theorem..................... 79 6.2 Automorphism schemes..................... 90 6.3 Tits-style classification..................... 93 7 Constructions with regular degenerate quadratic forms 108 7.1 Regular degenerate quadratic forms .............. 109 7.2 Conformal isometries...................... 121 7.3 Severi-Brauer varieties..................... 130 8 Constructions when 0 has a double bond 138 8.1 Additional constructions for type B............... 138 8.2 Constructions for type C.................... 144 8.3 Exceptional construction for rank 2............... 154 8.4 Generalized exotic groups ................... 162 8.5 Structure of Zq and Zg,c................... 166 9 Generalization of the standard construction 171 9.1 Generalized standard groups.................. 171 9.2 Structure theorem........................ 179 A Pseudo-isogenies 181 A.l Main result........................... 181 A.2 Proof of Pseudo-Isogeny Theorem............... 182 A. 3 Relation with the semisimple case............... 185 B Clifford constructions 187 B. l TypeB.............................. 188 B.2 Type C.............................. 189 B.3 Cases with [k : k 2 ] ^8..................... 190 B. 4 TypeBC............................. 197 C Pseudo-split and quasi-split forms 206 C. l General characteristic...................... 206 C.2 Quasi-split forms........................ 214 C.3 Rank-1 cases .......................... 226 C.4 Higher-rank and non-reduced cases............... 228
CONTENTS vii D Basic exotic groups of type F 4 of relative rank 2 230 D.l General preparations...................... 230 D.2 Forms of A:-rank 2........................ 233 Bibliography 239 Index 241
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| any_adam_object | 1 |
| author | Conrad, Brian 1970- Prasad, Gopal 1945- |
| author_GND | (DE-588)122429206 (DE-588)136265367 |
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| dewey-full | 512.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| dewey-search | 512.55 |
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| id | DE-604.BV042996157 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:25:13Z |
| institution | BVB |
| isbn | 9780691167923 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028421509 |
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| owner_facet | DE-19 DE-BY-UBM DE-20 DE-11 |
| physical | vii, 245 Seiten |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | Princeton University Press |
| record_format | marc |
| series | Annals of mathematics studies |
| series2 | Annals of mathematics studies |
| spellingShingle | Conrad, Brian 1970- Prasad, Gopal 1945- Classification of pseudo-reductive groups Annals of mathematics studies Linear algebraic groups Algebraische Gruppe (DE-588)4001164-1 gnd |
| subject_GND | (DE-588)4001164-1 |
| title | Classification of pseudo-reductive groups |
| title_auth | Classification of pseudo-reductive groups |
| title_exact_search | Classification of pseudo-reductive groups |
| title_full | Classification of pseudo-reductive groups Brian Conrad, Gopal Prasad |
| title_fullStr | Classification of pseudo-reductive groups Brian Conrad, Gopal Prasad |
| title_full_unstemmed | Classification of pseudo-reductive groups Brian Conrad, Gopal Prasad |
| title_short | Classification of pseudo-reductive groups |
| title_sort | classification of pseudo reductive groups |
| topic | Linear algebraic groups Algebraische Gruppe (DE-588)4001164-1 gnd |
| topic_facet | Linear algebraic groups Algebraische Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028421509&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000991 |
| work_keys_str_mv | AT conradbrian classificationofpseudoreductivegroups AT prasadgopal classificationofpseudoreductivegroups |