Download Algebraic Groups: The Theory of Group Schemes of Finite Type by J. S. Milne PDF

By J. S. Milne

Algebraic teams play a lot an identical function for algebraists as Lie teams play for analysts. This e-book is the 1st finished advent to the speculation of algebraic team schemes over fields that incorporates the constitution idea of semisimple algebraic teams, and is written within the language of recent algebraic geometry. the 1st 8 chapters learn common algebraic team schemes over a box and culminate in an evidence of the Barsotti–Chevalley theorem, understanding each algebraic team as an extension of an abelian type by way of an affine crew. After a overview of the Tannakian philosophy, the writer offers brief bills of Lie algebras and finite staff schemes. The later chapters deal with reductive algebraic teams over arbitrary fields, together with the Borel–Chevalley constitution conception. Solvable algebraic teams are studied intimately. must haves have additionally been saved to a minimal in order that the booklet is offered to non-specialists in algebraic geometry.

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