Overview

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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9780511661143

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Reviews

'This book is an impressive piece of work; many hard technical difficulties are overcome in order to provide the general structure of pseudo-reductive groups and to elucidate their classification by means of reasonable data. In view of the importance of this class of algebraic groups ... and of the impact of a better understanding of them on the general theory of linear algebraic groups, this book can be considered a fundamental reference in the area.' Mathematical Reviews 'Researchers and graduate students working in related areas, such as algebraic geometry, algebraic group theory, or number theory will appreciate this book and find many deep ideas, results and technical tools that may be used in other branches of mathematics.' Zentralbaltt MATH This book is an impressive piece of work; many hard technical difficulties are overcome in order to provide the general structure of pseudo-reductive groups and to elucidate their classification by means of reasonable data. In view of the importance of this class of algebraic groups and of the impact of a better understanding them on the general theory of linear algebraic groups, this book can be considered a fundamental reference in the area. Bertrand Remy, Mathematical Reviews

'This book is an impressive piece of work; many hard technical difficulties are overcome in order to provide the general structure of pseudo-reductive groups and to elucidate their classification by means of reasonable data. In view of the importance of this class of algebraic groups ... and of the impact of a better understanding of them on the general theory of linear algebraic groups, this book can be considered a fundamental reference in the area.' Mathematical Reviews 'Researchers and graduate students working in related areas, such as algebraic geometry, algebraic group theory, or number theory will appreciate this book and find many deep ideas, results and technical tools that may be used in other branches of mathematics.' Zentralbaltt MATH

'This book is an impressive piece of work; many hard technical difficulties are overcome in order to provide the general structure of pseudo-reductive groups and to elucidate their classification by means of reasonable data. In view of the importance of this class of algebraic groups … and of the impact of a better understanding of them on the general theory of linear algebraic groups, this book can be considered a fundamental reference in the area.' Mathematical Reviews 'Researchers and graduate students working in related areas, such as algebraic geometry, algebraic group theory, or number theory will appreciate this book and find many deep ideas, results and technical tools that may be used in other branches of mathematics.' Zentralbaltt MATH

Author Information

Brian Conrad is a Professor in the Department of Mathematics at Stanford University. Ofer Gabber is Professor of Mathematics at the Institut des Hautes Études Scientifiques (IHÉS), France. Gopal Prasad is Raoul Bott Professor of Mathematics at the University of Michigan.

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