Coverart for item
The Resource Classification of pseudo-reductive groups, Brian Conrad, Gopal Prasad

Classification of pseudo-reductive groups, Brian Conrad, Gopal Prasad

Label
Classification of pseudo-reductive groups
Title
Classification of pseudo-reductive groups
Statement of responsibility
Brian Conrad, Gopal Prasad
Creator
Contributor
Subject
Genre
Language
eng
Summary
In the earlier monograph Pseudo-reductive Groups, Brian Conrad, Ofer Gabber, and Gopal Prasad explored the general structure of pseudo-reductive groups. In this new book, Classification of Pseudo-reductive Groups, Conrad and Prasad go further to study the classification over an arbitrary field. An isomorphism theorem proved here determines the automorphism schemes of these groups. The book also gives a Tits-Witt type classification of isotropic groups and displays a cohomological obstruction to the existence of pseudo-split forms. Constructions based on regular degenerate quadratic forms and new techniques with central extensions provide insight into new phenomena in characteristic 2, which also leads to simplifications of the earlier work. A generalized standard construction is shown to account for all possibilities up to mild central extensions. The results and methods developed in Classification of Pseudo-reductive Groups will interest mathematicians and graduate students who work with algebraic groups in number theory and algebraic geometry in positive characteristic
Member of
Cataloging source
YDXCP
http://library.link/vocab/creatorDate
1970-
http://library.link/vocab/creatorName
Conrad, Brian
Index
index present
Language note
In English
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
Prasad, Gopal
Series statement
Annals of mathematics studies
Series volume
number 191
http://library.link/vocab/subjectName
  • Linear algebraic groups
  • Group theory
  • Geometry, Algebraic
  • Geometry, Algebraic
  • Group theory
  • Linear algebraic groups
  • MATHEMATICS
  • MATHEMATICS
Label
Classification of pseudo-reductive groups, Brian Conrad, Gopal Prasad
Instantiates
Publication
Copyright
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Cover; Title; Copyright; Contents; 1 Introduction; 1.1 Motivation; 1.2 Root systems and new results; 1.3 Exotic groups and degenerate quadratic forms; 1.4 Tame central extensions; 1.5 Generalized standard groups; 1.6 Minimal type and general structure theorem; 1.7 Galois-twisted forms and Tits classification; 1.8 Background, notation, and acknowledgments; 2 Preliminary notions; 2.1 Standard groups, Mevi subgroups, and root systems; 2.2 The basic exotic construction; 2.3 Minimal type; 3 Field-theoretic and linear-algebraic invariants; 3.1 A non-standard rank-1 construction
  • 3.2 Minimal field of definition for Ru(Gk̅)3.3 Root field and applications; 3.4 Application to classification results; 4 Central extensions and groups locally of minimal type; 4.1 Central quotients; 4.2 Beyond the quadratic case; 4.3 Groups locally of minimal type; 5 Universal smooth k-tame central extension; 5.1 Construction of central extensions; 5.2 A universal construction; 5.3 Properties and applications of ̃G; 6 Automorphisms, isomorphisms, and Tits classification; 6.1 Isomorphism Theorem; 6.2 Automorphism schemes; 6.3 Tits-style classification
  • B Clifford constructionsB.1 Type B; B.2 Type C; B.3 Cases with [k : k̂2] d"8; B.4 Type BC; C Pseudo-split and quasi-split forms; C.1 General characteristic; C.2 Quasi-split forms; C.3 Rank-1 cases; C.4 Higher-rank and non-reduced cases; D Basic exotic groups of type F4 of relative rank 2; D.1 General preparations; D.2 Forms of k-rank 2; Bibliography; Index
Control code
ocn930040951
Dimensions
unknown
Extent
1 online resource (1 volume)
Form of item
online
Isbn
9781400874026
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Note
JSTOR
Other control number
10.1515/9781400874026
http://library.link/vocab/ext/overdrive/overdriveId
  • 832712
  • 22573/ctt193f7hw
Specific material designation
remote
System control number
(OCoLC)930040951
Label
Classification of pseudo-reductive groups, Brian Conrad, Gopal Prasad
Publication
Copyright
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Cover; Title; Copyright; Contents; 1 Introduction; 1.1 Motivation; 1.2 Root systems and new results; 1.3 Exotic groups and degenerate quadratic forms; 1.4 Tame central extensions; 1.5 Generalized standard groups; 1.6 Minimal type and general structure theorem; 1.7 Galois-twisted forms and Tits classification; 1.8 Background, notation, and acknowledgments; 2 Preliminary notions; 2.1 Standard groups, Mevi subgroups, and root systems; 2.2 The basic exotic construction; 2.3 Minimal type; 3 Field-theoretic and linear-algebraic invariants; 3.1 A non-standard rank-1 construction
  • 3.2 Minimal field of definition for Ru(Gk̅)3.3 Root field and applications; 3.4 Application to classification results; 4 Central extensions and groups locally of minimal type; 4.1 Central quotients; 4.2 Beyond the quadratic case; 4.3 Groups locally of minimal type; 5 Universal smooth k-tame central extension; 5.1 Construction of central extensions; 5.2 A universal construction; 5.3 Properties and applications of ̃G; 6 Automorphisms, isomorphisms, and Tits classification; 6.1 Isomorphism Theorem; 6.2 Automorphism schemes; 6.3 Tits-style classification
  • B Clifford constructionsB.1 Type B; B.2 Type C; B.3 Cases with [k : k̂2] d"8; B.4 Type BC; C Pseudo-split and quasi-split forms; C.1 General characteristic; C.2 Quasi-split forms; C.3 Rank-1 cases; C.4 Higher-rank and non-reduced cases; D Basic exotic groups of type F4 of relative rank 2; D.1 General preparations; D.2 Forms of k-rank 2; Bibliography; Index
Control code
ocn930040951
Dimensions
unknown
Extent
1 online resource (1 volume)
Form of item
online
Isbn
9781400874026
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Note
JSTOR
Other control number
10.1515/9781400874026
http://library.link/vocab/ext/overdrive/overdriveId
  • 832712
  • 22573/ctt193f7hw
Specific material designation
remote
System control number
(OCoLC)930040951

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