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Algebraic groups[electronic resource...

Milne, J. S.

Algebraic groups[electronic resource] :the theory of group schemes of finite type over a field /

紀錄類型:	書目-電子資源 : Monograph/item
杜威分類號:	516.35
書名/作者:	Algebraic groups : the theory of group schemes of finite type over a field // J. S. Milne.
作者:	Milne, J. S.
出版者:	Cambridge : : Cambridge University Press,, 2017.
面頁冊數:	xvi, 644 p. : : digital ;; 24 cm.
附註:	Title from publisher's bibliographic system (viewed on 24 Oct 2017).
標題:	Linear algebraic groups.
標題:	Group theory.
ISBN:	9781316711736
ISBN:	9781107167483
摘要、提要註:	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.
電子資源:	https://doi.org/10.1017/9781316711736

Algebraic groups[electronic resource] :the theory of group schemes of finite type over a field /
Milne, J. S.

Algebraic groupsthe theory of group schemes of finite type over a field /[electronic resource] :J. S. Milne. - Cambridge :Cambridge University Press,2017. - xvi, 644 p. :digital ;24 cm. - Cambridge studies in advanced mathematics ;170. - Cambridge studies in advanced mathematics ;105..

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: 9781316711736Subjects--Topical Terms:

443168
Linear algebraic groups.

LC Class. No.: QA179 / .M55 2017

Dewey Class. No.: 516.35

Algebraic groups[electronic resource] :the theory of group schemes of finite type over a field /
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020 $a 9781107167483 $q (paper)
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050 4 $a QA179 $b .M55 2017
082 0 4 $a 516.35 $2 23
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100 1 $a Milne, J. S. $3 712144
245 1 0 $a Algebraic groups $h [electronic resource] : $b the theory of group schemes of finite type over a field / $c J. S. Milne.
260 $a Cambridge : $b Cambridge University Press, $c 2017.
300 $a xvi, 644 p. : $b digital ; $c 24 cm.
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 443168
650 0 $a Group theory. $3 404655
830 0 $a Cambridge studies in advanced mathematics ; $v 105. $3 642377
856 4 0 $u https://doi.org/10.1017/9781316711736

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