Algebraic Groups: The Theory of Group Schemes of Finite Type Over a Field (Cambridge Studies in Advanced Mathematics #170) (Hardcover)

Algebraic Groups: The Theory of Group Schemes of Finite Type Over a Field (Cambridge Studies in Advanced Mathematics #170) By J. S. Milne Cover Image
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Description


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.


Product Details
ISBN: 9781107167483
ISBN-10: 1107167485
Publisher: Cambridge University Press
Publication Date: September 21st, 2017
Pages: 660
Language: English
Series: Cambridge Studies in Advanced Mathematics