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

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 finished advent to the speculation of algebraic staff 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 learn normal algebraic workforce schemes over a box and culminate in an explanation of the Barsotti–Chevalley theorem, knowing each algebraic team as an extension of an abelian sort by way of an affine workforce. After a evaluate of the Tannakian philosophy, the writer offers brief debts 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. necessities have additionally been stored to a minimal in order that the e-book is obtainable to non-specialists in algebraic geometry.

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