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Pseudo-reductive groups / Brian Conrad, Stanford University, Ofer Gabber, Institut des hautes études scientifiques, Gopal Prasad, University of Michigan.

By: Conrad, Brian, 1970- [author.].
Contributor(s): Gabber, Ofer, 1958- [author.] | Prasad, Gopal [author.].
Material type: TextTextSeries: New mathematical monographs.Publisher: Cambridge ; New York : Cambridge University Press, [2015]Edition: Second edition.Description: xxiv, 665 pages; UKP 97.99 24 cms.Content type: text Media type: unmediated Carrier type: volumeISBN: 9781107087231 (hardback).Subject(s): Linear algebraic groups | Group theory | MATHEMATICS / Algebra / GeneralDDC classification: 512/.55 Other classification: MAT002000 Online resources: Cover image
Contents:
Machine generated contents note: 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.
Summary: "Pseudo-reductive groups arise naturally in the study of general smooth linear algebraic groups over non-perfect fields and have many important applications. This monograph provides a comprehensive treatment of the theory of pseudo-reductive groups and gives their classification in a usable form. In this second edition there is new material on relative root systems and Tits systems for general smooth affine groups, including the extension to quasi-reductive groups of famous simplicity results of Tits in the semisimple case. Chapter 9 has been completely rewritten to describe and classify pseudo-split absolutely pseudo-simple groups with a non-reduced root system over arbitrary fields of characteristic 2 via the useful new notion of 'minimal type' for pseudo-reductive groups. Researchers and graduate students working in related areas, 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.
List(s) this item appears in: 2018-10-19

Machine generated contents note: 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.

"Pseudo-reductive groups arise naturally in the study of general smooth linear algebraic groups over non-perfect fields and have many important applications. This monograph provides a comprehensive treatment of the theory of pseudo-reductive groups and gives their classification in a usable form. In this second edition there is new material on relative root systems and Tits systems for general smooth affine groups, including the extension to quasi-reductive groups of famous simplicity results of Tits in the semisimple case. Chapter 9 has been completely rewritten to describe and classify pseudo-split absolutely pseudo-simple groups with a non-reduced root system over arbitrary fields of characteristic 2 via the useful new notion of 'minimal type' for pseudo-reductive groups. Researchers and graduate students working in related areas, 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.