Pseudo-reductive Groups (New Mathematical Monographs)

Pseudo-reductive Groups (New Mathematical Monographs)

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Brian Conrad, Ofer Gabber, Gopal Prasad
Cambridge University Press
Edition: 2, 6/4/2015
EAN 9781107087231, ISBN10: 1107087236

Hardcover, 690 pages, 22.8 x 15.2 x 4.8 cm
Language: English

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.

Preface to the second edition
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