Download e-book for iPad: Algebraic Groups: The Theory of Group Schemes of Finite Type by J. S. Milne

By J. S. Milne

Algebraic teams play a lot an identical function for algebraists as Lie teams play for analysts. This booklet is the 1st entire creation to the speculation of algebraic crew schemes over fields that comes with the constitution thought of semisimple algebraic teams, and is written within the language of contemporary algebraic geometry. the 1st 8 chapters examine normal algebraic staff schemes over a box and culminate in an evidence of the Barsotti–Chevalley theorem, figuring out each algebraic workforce as an extension of an abelian sort through an affine team. After a evaluate of the Tannakian philosophy, the writer presents brief debts of Lie algebras and finite team schemes. The later chapters deal with reductive algebraic teams over arbitrary fields, together with the Borel–Chevalley constitution thought. Solvable algebraic teams are studied intimately. necessities have additionally been saved to a minimal in order that the publication is available to non-specialists in algebraic geometry.

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