Pseudo-reductive groups:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY [u.a.]
Cambridge Univ. Press
2010
|
| Edition: | 1. publ. |
| Series: | New mathematical monographs
17 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XX, 533 S. |
| ISBN: | 9780521195607 |
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MARC
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| 245 | 1 | 0 | |a Pseudo-reductive groups |c Brian Conrad ; Ofer Gabber ; Gopal Prasad |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a New York, NY [u.a.] |b Cambridge Univ. Press |c 2010 | |
| 300 | |a XX, 533 S. | ||
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Record in the Search Index
| _version_ | 1804145575781728256 |
|---|---|
| adam_text | Contents
Introduction page
xi
Terminology,
conventions, and notation
xix
Part
I
Constructions, examples, and structure
theory
1
1
Overview of pseudo-reductivity
3
1.1
Comparison with the reductive case
3
1.2
Elementary properties of pseudo-reductive groups
11
1.3
Preparations for the standard construction
16
1.4
The standard construction and examples
25
1.5
Main result
34
1.6
Weil restriction and fields of definition
36
2
Root groups and root systems
43
2.1
Limits associated to
1
-parameter subgroups
43
2.2
Pseudo-parabolic subgroups
59
2.3
Root groups in pseudo-reductive groups
67
2.4
Representability of automorphism functors
78
3
Basic structure theory
86
3.1
Perfect normal subgroups of pseudo-reductive groups
86
3.2
Root datum for pseudo-reductive groups
94
3.3
Unipotent groups associated to semigroups of roots
99
3.4
Bruhat decomposition and
Levi
subgroups
114
3.5
Classification of pseudo-parabolic subgroups
130
vn
viii Contents
Partii Standard
presentations and their
applications
147
4
Variation of
(G ,
k /k, T , C)
149
4.1
Absolutely simple and simply connected fibers
149
4.2
Uniqueness of (G , k /k)
154
5
Ubiquity of the standard construction
162
5.1
Main theorem and central extensions
162
5.2
Properties of standardness and standard presentations
170
5.3
A standardness criterion
179
6
Classification results
191
6.1
The
Α ι
-case away from characteristic
2 192
6.2
Types A2 and G2 away from characteristic
3 198
6.3
General cases away from characteristics
2
and
3 203
Partili
General classification and applications
215
7
The exotic constructions
217
7.1
Calculations in characteristics
2
and
3 217
7.2
Basic exotic pseudo-reductive groups
228
7.3
Algebraic and arithmetic aspects of basic exotic
pseudo-reductive groups
240
8
Preparations for classification in
characteristics
2
and
3 255
8.1
Further properties of basic exotic
pseudo-reductive groups
255
8.2
Exceptional and exotic pseudo-reductive groups
260
9
The absolutely pseudo-simple groups in characteristic
2 279
9.1
Type A!
280
9.2
Root groups and
birational
group laws
290
9.3
Construction of absolutely pseudo-simple groups with
a non-reduced root system
299
9.4
Classification of absolutely pseudo-simple groups with
a non-reduced root system
318
10
General case
342
10.1
Factors with non-reduced root system and the generalized
standard construction
342
10.2
Classification via generalized standard groups
351
Contents
11 Applications 358
11.1 Maximal
tori in
pseudo-reductive
groups
358
11.2 Pseudo-semisimplicity 364
11.3 Unirationality 368
11.4
Structure of root groups and pseudo-parabolic subgroups
372
Part IV Appendices
389
A Background in linear algebraic groups
391
A.I Review of definitions
392
A.
2
Some results from the general theory
398
A.3 Frobenius morphisms and non-aftine groups
402
A.
4
Split reductive groups: Existence, Isomorphism, and Isogeny
Theorems
407
A.
5
Weil restriction generalities
422
A.
6
Groups without
Levi
subgroups
441
A.
7
Lie algebras and Weil restriction
446
A.
8
Lie algebras and groups of multiplicative type
457
В
Tits work on unipotent groups in nonzero characteristic
473
B.I Subgroups of vector groups
473
B.2 Wound unipotent groups
479
B.3 The ccK/j-kernel
482
B.4 Torus actions on unipotent groups
485
С
Rational conjugacy in connected groups
494
C.
1
Pseudo-completeness
494
C.2 Conjugacy results in the smooth
affine case
504
C.3 Split unipotent subgroups of pseudo-reductive groups
511
C.4 Beyond the smooth
affine case
519
References
525
Index
527
|
| any_adam_object | 1 |
| author | Conrad, Brian 1970- Gabber, Ofer 1958- Prasad, Gopal 1945- |
| author_GND | (DE-588)122429206 (DE-588)124938922 (DE-588)136265367 |
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| author_sort | Conrad, Brian 1970- |
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| classification_rvk | SK 260 |
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| discipline | Mathematik |
| edition | 1. publ. |
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| id | DE-604.BV026936340 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T23:21:38Z |
| institution | BVB |
| isbn | 9780521195607 |
| language | English |
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| oclc_num | 756277990 |
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| owner | DE-188 DE-703 DE-91G DE-BY-TUM DE-20 |
| owner_facet | DE-188 DE-703 DE-91G DE-BY-TUM DE-20 |
| physical | XX, 533 S. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | New mathematical monographs |
| series2 | New mathematical monographs |
| spelling | Conrad, Brian 1970- Verfasser (DE-588)122429206 aut Pseudo-reductive groups Brian Conrad ; Ofer Gabber ; Gopal Prasad 1. publ. New York, NY [u.a.] Cambridge Univ. Press 2010 XX, 533 S. txt rdacontent n rdamedia nc rdacarrier New mathematical monographs 17 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 DE-604 Gabber, Ofer 1958- Verfasser (DE-588)124938922 aut Prasad, Gopal 1945- Verfasser (DE-588)136265367 aut New mathematical monographs 17 (DE-604)BV035420183 17 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022457895&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Conrad, Brian 1970- Gabber, Ofer 1958- Prasad, Gopal 1945- Pseudo-reductive groups New mathematical monographs 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 ; 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 | Lineare algebraische Gruppe (DE-588)4295326-1 gnd Reduktive Gruppe (DE-588)4177313-5 gnd |
| topic_facet | Lineare algebraische Gruppe Reduktive Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022457895&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035420183 |
| work_keys_str_mv | AT conradbrian pseudoreductivegroups AT gabberofer pseudoreductivegroups AT prasadgopal pseudoreductivegroups |