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

Author: J S Milne
Publisher: Cambridge, United Kingdom ; New York, New York : Cambridge University Press, 2017. ©2017
Series: Cambridge studies in advanced mathematics, 170.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
"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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Milne, J.S., 1942-
Algebraic groups.
Cambridge, United Kingdom ; New York, New York: Cambridge University Press, [2017]
(OCoLC)992433996
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: J S Milne
ISBN: 9781316711736 1316711730
OCLC Number: 1004615128
Description: 1 online resource (xiv, 644 pages) : illustrations
Contents: Definitions and basic properties --
Examples and basic constructions --
Affine algebraic groups and Hopf algebras --
Linear representations of algebraic groups --
Group theory: the isomorphism theorems --
Subnormal series; solvable and nilpotent algebraic groups --
Algebraic groups acting on schemes --
The structure of general algebraic groups --
The structure of general algebraic groups --
Tannaka duality; Jordan decompositions --
The Lie algebra of an algebraic group --
Finite group schemes --
Groups of multiplicative type; linearly reductive groups --
Tori acting on schemes --
Unipotent algebraic groups --
Cohomology and extensions --
The structure of solvable algebraic groups --
Borel subgroups and applications --
The geometry of algebraic groups --
Semisimple and reductive groups --
Algebraic groups of semisimple rank one --
Split reductive groups --
Representations of reductive groups --
The isogeny and existence theorems --
Construction of the semisimple groups --
Additional topics.
Series Title: Cambridge studies in advanced mathematics, 170.
Responsibility: J.S. Milne, University of Michigan, Ann Arbor.

Abstract:

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  Read more...

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'All together, this excellent text fills a long-standing gap in the textbook literature on algebraic groups. It presents the modern theory of group schemes in a very comprehensive, systematic, Read more...

 
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