Algebraic Groups

The Theory of Group Schemes of Finite Type over a Field

Nonfiction, Science & Nature, Mathematics, Topology, Algebra
Cover of the book Algebraic Groups by J. S. Milne, Cambridge University Press
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: J. S. Milne ISBN: 9781316733363
Publisher: Cambridge University Press Publication: September 21, 2017
Imprint: Cambridge University Press Language: English
Author: J. S. Milne
ISBN: 9781316733363
Publisher: Cambridge University Press
Publication: September 21, 2017
Imprint: Cambridge University Press
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Cambridge University Press

Cover of the book Convex Optimization by J. S. Milne
Cover of the book Social Rights Jurisprudence by J. S. Milne
Cover of the book White Matter Dementia by J. S. Milne
Cover of the book The Logic of Connective Action by J. S. Milne
Cover of the book Fluid Dynamics by J. S. Milne
Cover of the book Imperial Unknowns by J. S. Milne
Cover of the book The Ancient Greek Economy by J. S. Milne
Cover of the book Shell Shock, Memory, and the Novel in the Wake of World War I by J. S. Milne
Cover of the book Saul Kripke by J. S. Milne
Cover of the book Supports in Roman Marble Sculpture by J. S. Milne
Cover of the book Power and the Vote by J. S. Milne
Cover of the book The Cambridge Handbook of Surveillance Law by J. S. Milne
Cover of the book Human Rights and Social Work by J. S. Milne
Cover of the book Harmonic and Subharmonic Function Theory on the Hyperbolic Ball by J. S. Milne
Cover of the book Human Development in the Life Course by J. S. Milne
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy