Algebraic Groups

Algebraic Groups by J S Milne

Algebraic groups play much the same role for algebraists as Lie groups play for analysts. This book is the first comprehensive introduction to the theory of algebraic group schemes over fields that includes the structure theory of semisimple algebraic groups, and is written in the language of modern algebraic geometry. The first eight chapters study general algebraic group schemes over a field and culminate in a proof of the Barsotti–Chevalley theorem, realizing every algebraic group as an extension of an abelian variety by an affine group. After a review of the Tannakian philosophy, the author provides short accounts of Lie algebras and finite group schemes. The later chapters treat reductive algebraic groups over arbitrary fields, including the Borel–Chevalley structure theory. Solvable algebraic groups are studied in detail. Prerequisites have also been kept to a minimum so that the book is accessible to non-specialists in algebraic geometry.

'All together, this excellent text fills a long-standing gap in the textbook literature on algebraic groupsIt presents the modern theory of group schemes in a very comprehensive, systematic, detailed and lucid manner, with numerous illustrating examples and exercises. It is fair to say that this reader-friendly textbook on algebraic groups is the long-desired modern successor to the old, venerable standard primers …' Werner Kleinert, zbMath
'The author invests quite a lot to make difficult things understandable, and as a result, it is a real pleasure to read the book. All in all, with no doubt, Milne's new book will remain for decades an indispensable source for everybody interested in algebraic groups.' Boris È. Kunyavskiĭ, MathSciNet

J. S. Milne is Professor Emeritus at the University of Michigan, Ann Arbor. His previous books include Etale Cohomology (1980) and Arithmetic Duality Theorems (2006).

SKU	Unavailable
ISBN 13	9781009018586
ISBN 10	1009018582
Title	Algebraic Groups
Author	J S Milne
Series	Cambridge Studies In Advanced Mathematics
Condition	Unavailable
Binding Type	Paperback
Publisher	Cambridge University Press
Year published	2022-06-30
Number of pages	664
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
Note	Unavailable