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 position for algebraists as Lie teams play for analysts. This e-book is the 1st entire creation to the speculation of algebraic team schemes over fields that comes with the constitution thought of semisimple algebraic teams, and is written within the language of recent algebraic geometry. the 1st 8 chapters examine basic algebraic workforce schemes over a box and culminate in an evidence of the Barsotti–Chevalley theorem, understanding each algebraic workforce as an extension of an abelian kind through an affine crew. After a overview of the Tannakian philosophy, the writer offers brief bills of Lie algebras and finite workforce schemes. The later chapters deal with reductive algebraic teams over arbitrary fields, together with the Borel–Chevalley constitution concept. Solvable algebraic teams are studied intimately. must haves have additionally been stored to a minimal in order that the booklet is offered to non-specialists in algebraic geometry.

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