Pseudo-reductive Groups

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August 2010



A comprehensive treatment of the theory. Includes numerous new results and a complete classification.


Introduction; Terminology, conventions, and notation; Part I. Constructions, Examples, and Structure Theory: 1. Overview of pseudo-reductivity; 2. Root groups and root systems; 3. Basic structure theory; Part II. Standard Presentations and Their Applications: 4. Variation of (G', k'/k, T', C); 5. Universality of the standard construction; 6. Classification results; Part III. General Classification and Applications: 7. General classification and applications; 8. Preparations for classification in characteristics 2 and 3; 9. The absolutely pseudo-simple case in characteristic 2; 10. General case; 11. Applications; Part IV. Appendices: A. Background in linear algebraic groups; B. Tits' work on unipotent groups in nonzero characteristic; C. Rational conjugacy in connected groups; References; Index.


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


'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
EAN: 9780521195607
ISBN: 0521195608
Untertitel: 'New Mathematical Monographs'. Sprache: Englisch.
Erscheinungsdatum: August 2010
Seitenanzahl: 533 Seiten
Format: gebunden
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