Algebraic groups Elektronische Ressource the theory of group schemes of finite type over a field J. S. Milne

By: Milne, J. S [VerfasserIn]
Material type: TextTextLanguage: English Series: Cambridge studies in advanced mathematics 170Publisher: Cambridge New York Port Melbourne Delhi Singapore Cambridge University Press 2017Description: 1 Online-Ressource (xvi, 644 Seiten)Content type: Text Media type: Computermedien Carrier type: Online-RessourceISBN: 9781316711736; 9781107167483 (print)Subject(s): Linear algebraic groups | Group theory | Group theory | Linear algebraic groupsAdditional physical formats: Print version: No titleDDC classification: 516/.35 LOC classification: QA179Online resources: Volltext 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 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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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

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