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Algebraic groups : = the theory of group schemes of finite type over a field /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Algebraic groups :/ J. S. Milne.
Reminder of title:	the theory of group schemes of finite type over a field /
Author:	Milne, J. S.,
Description:	1 online resource (xvi, 644 pages) :digital, PDF file(s). :
Notes:	Title from publisher's bibliographic system (viewed on 24 Oct 2017).
Subject:	Linear algebraic groups. -
Online resource:	https://doi.org/10.1017/9781316711736
ISBN:	9781316711736 (ebook)

Algebraic groups : = the theory of group schemes of finite type over a field /
Milne, J. S.,1942-

Algebraic groups :the theory of group schemes of finite type over a field /J. S. Milne. - 1 online resource (xvi, 644 pages) :digital, PDF file(s). - Cambridge studies in advanced mathematics ;170. - Cambridge studies in advanced mathematics ;134..

Title from publisher's bibliographic system (viewed on 24 Oct 2017).

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.

ISBN: 9781316711736 (ebook)Subjects--Topical Terms:

672180
Linear algebraic groups.

LC Class. No.: QA179 / .M55 2017

Dewey Class. No.: 516/.35

Algebraic groups : = the theory of group schemes of finite type over a field /
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490 1 $a Cambridge studies in advanced mathematics ; $v 170
500 $a Title from publisher's bibliographic system (viewed on 24 Oct 2017).
520 $a 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.
650 0 $a Linear algebraic groups. $3 672180
650 0 $a Group theory. $3 527791
776 0 8 $i Print version: $z 9781107167483
830 0 $a Cambridge studies in advanced mathematics ; $v 134. $3 1133579
856 4 0 $u https://doi.org/10.1017/9781316711736