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

By J. S. Milne

Algebraic teams play a lot a similar position for algebraists as Lie teams play for analysts. This publication is the 1st finished advent to the speculation of algebraic crew schemes over fields that incorporates the constitution concept of semisimple algebraic teams, and is written within the language of contemporary algebraic geometry. the 1st 8 chapters research normal algebraic staff schemes over a box and culminate in an evidence of the Barsotti–Chevalley theorem, understanding each algebraic team as an extension of an abelian sort by means of an affine crew. After a evaluate of the Tannakian philosophy, the writer presents brief money owed 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. 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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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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