Conrad, Brian (Stanford University, California)

Pseudo-reductive Groups - New Mathematical Monographs Conrad, Brian (Stanford University, California) 2 Revised edition

Marc Notes: The theory of pseudo-reductive groups is required for the study of general linear algebraic groups over non-perfect fields. This treatment includes new results & a complete classification. The authors describe some of the important applications of the theory and provide a complete exposition of Tits' structure theory of unipotent groups. Brief Description: This monograph provides a comprehensive treatment of the theory of pseudo-reductive groups and gives their classification in a usable form. Table of Contents: Preface to the second edition; 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. Ubiquity of the standard construction; 6. Classification results; Part III. General Classification and Applications: 7. The exotic constructions; 8. Preparations for classification in characteristics 2 and 3; 9. Absolutely pseudo-simple groups 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. Review Quotes: Review of previous edition: '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 ReviewsReview Quotes: Review of previous edition: '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.' Zentralblatt MATH

Contributor Bio:  Conrad, Brian Brian Conrad is a Professor in the Department of Mathematics at Stanford University. Contributor Bio:  Gabber, Ofer Ofer Gabber is a Directeur de Recherches CNRS at the Institut des Hautes Etudes Scientifiques (IHES). Contributor Bio:  Prasad, Gopal Gopal Prasad is Raoul Bott Professor of Mathematics at the University of Michigan.