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

By J. S. Milne

Algebraic teams play a lot a similar position for algebraists as Lie teams play for analysts. This ebook is the 1st entire advent to the speculation of algebraic team schemes over fields that comes with the constitution conception of semisimple algebraic teams, and is written within the language of contemporary algebraic geometry. the 1st 8 chapters research basic algebraic workforce schemes over a box and culminate in an explanation of the Barsotti–Chevalley theorem, figuring out each algebraic workforce as an extension of an abelian kind via an affine workforce. After a overview of the Tannakian philosophy, the writer presents brief debts of Lie algebras and finite staff 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. must haves have additionally been stored to a minimal in order that the e-book is on the market to non-specialists in algebraic geometry.

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Algebraic Groups: The Theory of Group Schemes of Finite Type over a Field (Cambridge Studies in Advanced Mathematics) by J. S. Milne


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