Pseudo-reductive groups / Brian Conrad, Ofer Gabber, Gopal Prasad.

Format:

Book

Author/Creator:

Conrad, Brian, 1970- author.

Gabber, Ofer, 1958- author.

Prasad, Gopal, author.

Series:

Cambridge books online.

New mathematical monographs ; 17.

New mathematical monographs ; 17

Language:

English

Subjects (All):

Linear algebraic groups.

Group theory.

Physical Description:

1 online resource (xx, 533 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2010.

System Details:

text file

PDF

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 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.

Contents:

Constructions, examples, and structure theory. Overview of pseudo-reductivity ; Root groups and root systems ; Basic structure theory

Standard presentations and their applications. Variation of (G', k'/k, T', C) ; Ubiquity of the standard construction ; Classification results

General classification and applications. The exotic constructions ; Preparations for classification in characteristics 2 and 3 ; The absolutely pseudo-simple groups in characteristic 2 ; General case ; Applications

Appendices. Background in linear algebraic groups ; Tits' work on unipotent groups in nonzero characteristic ; Rational conjugacy in connected groups.

Notes:

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

Other Format:

Print version:

ISBN:

9780511661143

Access Restriction:

Restricted for use by site license.