Pseudo-reductive groups:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY [u.a.]
Cambridge Univ. Press
2010
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | New mathematical monographs
17 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XX, 533 S. |
| ISBN: | 9780521195607 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV026936340 | ||
| 003 | DE-604 | ||
| 005 | 20130913 | ||
| 007 | t | ||
| 008 | 110326s2010 |||| 00||| eng d | ||
| 020 | |a 9780521195607 |9 978-0-521-19560-7 | ||
| 035 | |a (OCoLC)756277990 | ||
| 035 | |a (DE-599)HBZHT016472676 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-188 |a DE-703 |a DE-91G |a DE-20 | ||
| 084 | |a SK 260 |0 (DE-625)143227: |2 rvk | ||
| 084 | |a MAT 204f |2 stub | ||
| 100 | 1 | |a Conrad, Brian |d 1970- |e Verfasser |0 (DE-588)122429206 |4 aut | |
| 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. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a New mathematical monographs |v 17 | |
| 650 | 0 | 7 | |a Lineare algebraische Gruppe |0 (DE-588)4295326-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Reduktive Gruppe |0 (DE-588)4177313-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Reduktive Gruppe |0 (DE-588)4177313-5 |D s |
| 689 | 0 | 1 | |a Lineare algebraische Gruppe |0 (DE-588)4295326-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Gabber, Ofer |d 1958- |e Verfasser |0 (DE-588)124938922 |4 aut | |
| 700 | 1 | |a Prasad, Gopal |d 1945- |e Verfasser |0 (DE-588)136265367 |4 aut | |
| 830 | 0 | |a New mathematical monographs |v 17 |w (DE-604)BV035420183 |9 17 | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u 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 |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-022457895 | ||
Datensatz im Suchindex
| _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 |
| author_facet | Conrad, Brian 1970- Gabber, Ofer 1958- Prasad, Gopal 1945- |
| author_role | aut aut aut |
| author_sort | Conrad, Brian 1970- |
| author_variant | b c bc o g og g p gp |
| building | Verbundindex |
| bvnumber | BV026936340 |
| classification_rvk | SK 260 |
| classification_tum | MAT 204f |
| ctrlnum | (OCoLC)756277990 (DE-599)HBZHT016472676 |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01686nam a2200409 cb4500</leader><controlfield tag="001">BV026936340</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20130913 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">110326s2010 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780521195607</subfield><subfield code="9">978-0-521-19560-7</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)756277990</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)HBZHT016472676</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-188</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-20</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 260</subfield><subfield code="0">(DE-625)143227:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 204f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Conrad, Brian</subfield><subfield code="d">1970-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)122429206</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Pseudo-reductive groups</subfield><subfield code="c">Brian Conrad ; Ofer Gabber ; Gopal Prasad</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">1. publ.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York, NY [u.a.]</subfield><subfield code="b">Cambridge Univ. Press</subfield><subfield code="c">2010</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XX, 533 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">New mathematical monographs</subfield><subfield code="v">17</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Lineare algebraische Gruppe</subfield><subfield code="0">(DE-588)4295326-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Reduktive Gruppe</subfield><subfield code="0">(DE-588)4177313-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Reduktive Gruppe</subfield><subfield code="0">(DE-588)4177313-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Lineare algebraische Gruppe</subfield><subfield code="0">(DE-588)4295326-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Gabber, Ofer</subfield><subfield code="d">1958-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)124938922</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Prasad, Gopal</subfield><subfield code="d">1945-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)136265367</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">New mathematical monographs</subfield><subfield code="v">17</subfield><subfield code="w">(DE-604)BV035420183</subfield><subfield code="9">17</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Bayreuth</subfield><subfield code="q">application/pdf</subfield><subfield code="u">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</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-022457895</subfield></datafield></record></collection> |
| id | DE-604.BV026936340 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T23:21:38Z |
| institution | BVB |
| isbn | 9780521195607 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-022457895 |
| oclc_num | 756277990 |
| open_access_boolean | |
| 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 |