عنوان

Pseudo-reductive groups /

(Number (ISBN

1107087236

(Number (ISBN

9781107087231

Number

dltt

Title Proper

Pseudo-reductive groups /

General Material Designation

[Book]

First Statement of Responsibility

Brian Conrad (Stanford University), Ofer Gabber (Institut des hautes études scientifiques), Gopal Prasad (University of Michigan).

Edition Statement

Second edition.

Specific Material Designation and Extent of Item

xxiv, 665 pages ;

Dimensions

24 cm.

Series Title

New mathematical monographs ;

Volume Designation

26

Text of Note

Includes bibliographical references (pages 656658) and index.

Text of Note

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.

0

Text of Note

"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"--

Group theory.

Linear algebraic groups.

Group theory.

Linear algebraic groups.

Lineare algebraische Gruppe.

MATHEMATICS / Algebra / General.

Reduktive Gruppe.

Class number

System Code

Conrad, Brian,1970-

Gabber, Ofer,1958-

Prasad, Gopal

Date of Transaction

20151124131238.0

Cataloguing Rules (Descriptive Conventions))

rda

Electronic name

[Book]

Y