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Author Conrad, Brian David, 1970-
Title Pseudo-reductive groups / Brian Conrad, Ofer Gabber, Gopal Prasad
Imprint Cambridge ; New York : Cambridge University Press, 2010
book jacket
 Mathematics Library  QA179 .C667 2010    AVAILABLE    30340200509945
Descript xx, 533 p. ; 24 cm
Series New mathematical monographs ; 17
New mathematical monographs ; 17
Note Includes bibliographical references and index
"Pseudo-reductive groups arise naturally in the study of general smooth linear algebraic groups over non-perfect fields and have many important applications. This self-contained monograph provides a comprehensive treatment of the theory of pseudo-reductive groups and gives their classification in a usable form. The authors present numerous new results and also give a complete exposition of Tits' structure theory of unipotent groups. They prove the conjugacy results (conjugacy of maximal split tori, minimal pseudo-parabolic subgroups, maximal split unipotent subgroups) announced by Armand Borel and Jacques Tits, and also give the Bruhat decomposition, of general smooth connected algebraic groups. Researchers and graduate students working in any related area, such as algebraic geometry, algebraic group theory, or number theory, will value this book as it develops tools likely to be used in tackling other problems"-- Provided by publisher
Constructions, examples, and structure theory. Overview of pseudo-reductivity ; Root groups and root systems ; Basic structure theory -- Standard presentations and their applications. Variation of (G', k'/k, T', C) ; Ubiquity of the standard construction ; Classification results -- General classification and applications. The exotic constructions ; Preparations for classification in characteristics 2 and 3 ; The absolutely pseudo-simple groups in characteristic 2 ; General case ; Applications -- Appendices. Background in linear algebraic groups ; Tits' work on unipotent groups in nonzero characteristic ; Rational conjugacy in connected groups
Subject Linear algebraic groups
Group theory
Alt Author Gabber, Ofer, 1958-
Prasad, Gopal
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