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" Pseudo-reductive groups / "
Brian Conrad, Ofer Gabber, Gopal Prasad
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BL
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| Record Number
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706206
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b528395
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| Main Entry
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Conrad, Brian,1970-
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| Title & Author
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Pseudo-reductive groups /\ Brian Conrad, Ofer Gabber, Gopal Prasad
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| Publication Statement
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Cambridge ;New York :: Cambridge University Press,, 2010
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| Series Statement
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New mathematical monographs ;; 17
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| Page. NO
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xx, 533 p. :: ill. ;; 24 cm
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| ISBN
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0521195608 (hbk.)
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: 9780521195607 (hbk.)
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| Bibliographies/Indexes
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Includes bibliographical references (p. 525-526) and index
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| Contents
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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
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| Abstract
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"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"--
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"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"--
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| Subject
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Group theory
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Linear algebraic groups
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| Dewey Classification
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512/.55
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| LC Classification
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QA179.C667 2010
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| Added Entry
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Gabber, Ofer,1958-
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Prasad, Gopal
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