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

Format:

Book

Author/Creator:

Conrad, Brian, 1970- author.

Gabber, Ofer, 1958- author.

Prasad, Gopal, author.

Series:

New mathematical monographs ; 26.

New mathematical monographs ; 26

Language:

English

Subjects (All):

Linear algebraic groups.

Group theory.

Physical Description:

1 online resource (xxiv, 665 pages) : digital, PDF file(s).

Edition:

Second edition.

Place of Publication:

Cambridge : Cambridge University Press, 2015.

Language Note:

English

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.

Contents:

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.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

ISBN:

1-316-28941-9

1-316-31007-8

1-316-32345-5

1-316-33013-3

1-316-33347-7

1-316-32679-9

1-316-09243-7

1-316-32009-X