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  3. Algebraic Groups
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    • Publisher:
      Cambridge University Press
      Publication date:
      25 October 2017
      21 September 2017
      ISBN:
      9781316711736
      9781107167483
      9781009018586
      DOI:
      https://doi.org/10.1017/9781316711736
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      1.05kg, 660 Pages
      Dimensions:
      (229 x 152 mm)
      Weight & Pages:
      1.06kg, 666 Pages
      • Subjects:
      Mathematics (general), Mathematics, Geometry and Topology, Algebra
      Series:
      Cambridge Studies in Advanced Mathematics (170)
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    Subjects:
    Mathematics (general), Mathematics, Geometry and Topology, Algebra
    Series:
    Cambridge Studies in Advanced Mathematics (170)
    Information

    Book description

    Algebraic groups play much the same role for algebraists as Lie groups play for analysts. This book is the first comprehensive introduction to the theory of algebraic group schemes over fields that includes the structure theory of semisimple algebraic groups, and is written in the language of modern algebraic geometry. The first eight chapters study general algebraic group schemes over a field and culminate in a proof of the Barsotti–Chevalley theorem, realizing every algebraic group as an extension of an abelian variety by an affine group. After a review of the Tannakian philosophy, the author provides short accounts of Lie algebras and finite group schemes. The later chapters treat reductive algebraic groups over arbitrary fields, including the Borel–Chevalley structure theory. Solvable algebraic groups are studied in detail. Prerequisites have also been kept to a minimum so that the book is accessible to non-specialists in algebraic geometry.

    Reviews

    'All together, this excellent text fills a long-standing gap in the textbook literature on algebraic groups. It presents the modern theory of group schemes in a very comprehensive, systematic, detailed and lucid manner, with numerous illustrating examples and exercises. It is fair to say that this reader-friendly textbook on algebraic groups is the long-desired modern successor to the old, venerable standard primers …'

    Werner Kleinert Source: zbMath

    'The author invests quite a lot to make difficult things understandable, and as a result, it is a real pleasure to read the book. All in all, with no doubt, Milne's new book will remain for decades an indispensable source for everybody interested in algebraic groups.'

    Boris È. Kunyavskiĭ Source: MathSciNet

    ‘… fulfills the dual purpose of providing an updated account of the theory of reductive groups while at the same time serving as an accessible entry point into the general theory of reductive group schemes.’

    Igor A. Rapinchuk Source: Bulletin of the American Mathematical Society

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    Contents

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    Contents

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    References

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