By J. S. Milne

ISBN-10: 1107167485

ISBN-13: 9781107167483

Algebraic teams play a lot an identical function for algebraists as Lie teams play for analysts. This booklet is the 1st complete creation to the idea of algebraic crew schemes over fields that comes with the constitution conception of semisimple algebraic teams, and is written within the language of recent algebraic geometry. the 1st 8 chapters learn basic algebraic crew schemes over a box and culminate in an evidence of the Barsotti–Chevalley theorem, knowing each algebraic workforce as an extension of an abelian style by way of an affine staff. After a evaluate of the Tannakian philosophy, the writer offers 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. necessities have additionally been stored to a minimal in order that the booklet is obtainable 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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