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



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Autore: Conrad Brian <1970-> Visualizza persona
Titolo: Classification of pseudo-reductive groups / / Brian Conrad, Gopal Prasad Visualizza cluster
Pubblicazione: Princeton, New Jersey ; ; Oxford, England : , : Princeton University Press, , 2016
©2016
Descrizione fisica: 1 online resource (256 p.)
Disciplina: 512/.55
Soggetto topico: Linear algebraic groups
Group theory
Geometry, Algebraic
Soggetto non controllato: "ient homomorphism
Cartan k-subgroup
Dynkin diagram
Isogeny Theorem
Isomorphism Theorem
Levi subgroup
SeveriЂrauer variety
Tits classification
Tits-style classification
Weil restriction
algebraic geometry
automorphism functor
automorphism scheme
automorphism
canonical central extensions
central "ient
central extension
characteristic 2.
conformal isometry
degenerate quadratic form
double bond
exotic construction
field-theoretic invariant
generalized exotic group
generalized standard group
generalized standard presentation
generalized standard
isomorphism class
isomorphism
isotropic group
k-tame central extension
linear isomorphism
linear-algebraic invariant
maximal torus
minimal type
non-reduced root system
number theory
pseudo-isogeny
pseudo-reductive group
pseudo-semisimple group
pseudo-simple group
pseudo-simple k-group
pseudo-split form
pseudo-split
quadratic space
quadrics
rank-1
rank-2
rigidity property
root field
root system
scheme-theoretic center
semisimple "ient
semisimple k-group
structure theorem
Persona (resp. second.): PrasadGopal
Note generali: Description based upon print version of record.
Nota di bibliografia: Includes bibliographical references and index.
Nota di contenuto: Front matter -- Contents -- 1. Introduction -- 2. Preliminary notions -- 3. Field-theoretic and linear-algebraic invariants -- 4. Central extensions and groups locally of minimal type -- 5. Universal smooth k-tame central extension -- 6. Automorphisms, isomorphisms, and Tits classification -- 7. Constructions with regular degenerate quadratic forms -- 8. Constructions when Φ has a double bond -- 9. Generalization of the standard construction -- A. Pseudo-isogenies -- B. Clifford constructions -- C. Pseudo-split and quasi-split forms -- D. Basic exotic groups of type F4 of relative rank 2 -- Bibliography -- Index
Sommario/riassunto: 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.
Titolo autorizzato: Classification of pseudo-reductive groups  Visualizza cluster
ISBN: 1-4008-7402-5
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910797511403321
Lo trovi qui: Univ. Federico II
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Serie: Annals of mathematics studies ; ; Number 191.