The Resource Classification of pseudo-reductive groups, Brian Conrad, Gopal Prasad
Classification of pseudo-reductive groups, Brian Conrad, Gopal Prasad
Resource Information
The item Classification of pseudo-reductive groups, Brian Conrad, Gopal Prasad represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of San Diego Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Classification of pseudo-reductive groups, Brian Conrad, Gopal Prasad represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of San Diego Libraries.
This item is available to borrow from 1 library branch.
- 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
- Language
- eng
- Extent
- 1 online resource (1 volume)
- 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
- Isbn
- 9781400874026
- Label
- Classification of pseudo-reductive groups
- Title
- Classification of pseudo-reductive groups
- Statement of responsibility
- Brian Conrad, Gopal Prasad
- 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
- 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
- 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
- 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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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.sandiego.edu/portal/Classification-of-pseudo-reductive-groups-Brian/_Ej3D1VCGkY/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.sandiego.edu/portal/Classification-of-pseudo-reductive-groups-Brian/_Ej3D1VCGkY/">Classification of pseudo-reductive groups, Brian Conrad, Gopal Prasad</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.sandiego.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.sandiego.edu/">University of San Diego Libraries</a></span></span></span></span></div>
