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Algebraic Groups: The Theory of Group Schemes of Finite Type - download pdf or read online

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By J. S. Milne

Algebraic teams play a lot an analogous position for algebraists as Lie teams play for analysts. This booklet is the 1st accomplished advent to the idea of algebraic team schemes over fields that comes with the constitution concept of semisimple algebraic teams, and is written within the language of contemporary algebraic geometry. the 1st 8 chapters examine basic algebraic crew schemes over a box and culminate in an explanation of the Barsotti–Chevalley theorem, knowing each algebraic crew as an extension of an abelian style by way of an affine staff. 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 thought. Solvable algebraic teams are studied intimately. necessities have additionally been saved to a minimal in order that the booklet is offered 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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