Algebraic Groups (inbunden)
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Format
Häftad (Trade paperback)
Språk
Engelska
Serie
Cambridge Studies in Advanced Mathematics
Antal sidor
664
Utgivningsdatum
2022-06-30
Förlag
Cambridge University Press
Dimensioner
229 x 152 x 37 mm
Vikt
962 g
ISBN
9781009018586

Algebraic Groups

The Theory of Group Schemes of Finite Type over a Field

av J S Milne, J S Milne
Häftad,  Engelska, 2022-06-30
547
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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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Övrig information

J. S. Milne is Professor Emeritus at the University of Michigan, Ann Arbor. His previous books include Etale Cohomology (1980) and Arithmetic Duality Theorems (2006).

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