Algebraic Groups : The Theory of Group Schemes of Finite Type over a Field
by
J. S. Milne
Book Details
Format
Paperback / Softback
Book Series
Cambridge Studies in Advanced Mathematics
ISBN-10
1009018582
ISBN-13
9781009018586
Publisher
Cambridge University Press
Imprint
Cambridge University Press
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Jun 30th, 2022
Print length
664 Pages
Weight
1,060 grams
Dimensions
15.10 x 23.00 x 4.20 cms
Product Classification:
Groups & group theoryAlgebraic geometry
Ksh 8,850.00
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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.
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.
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