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  3. Pseudo-reductive Groups
  • Cited by 104
      • 2nd edition
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    • Publisher:
      Cambridge University Press
      Publication date:
      June 2015
      June 2015
      ISBN:
      9781316092439
      9781107087231
      DOI:
      https://doi.org/10.1017/CBO9781316092439
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      1.18kg, 690 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Number Theory, Algebra
      Series:
      New Mathematical Monographs (26)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Number Theory, Algebra
    Series:
    New Mathematical Monographs (26)
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    Book description

    Pseudo-reductive groups arise naturally in the study of general smooth linear algebraic groups over non-perfect fields and have many important applications. This monograph provides a comprehensive treatment of the theory of pseudo-reductive groups and gives their classification in a usable form. In this second edition there is new material on relative root systems and Tits systems for general smooth affine groups, including the extension to quasi-reductive groups of famous simplicity results of Tits in the semisimple case. Chapter 9 has been completely rewritten to describe and classify pseudo-split absolutely pseudo-simple groups with a non-reduced root system over arbitrary fields of characteristic 2 via the useful new notion of 'minimal type' for pseudo-reductive groups. Researchers and graduate students working in related areas, such as algebraic geometry, algebraic group theory, or number theory will value this book, as it develops tools likely to be used in tackling other problems.

    Reviews

    Review of previous edition:‘This book is an impressive piece of work; many hard technical difficulties are overcome in order to provide the general structure of pseudo-reductive groups and to elucidate their classification by means of reasonable data. In view of the importance of this class of algebraic groups … and of the impact of a better understanding of them on the general theory of linear algebraic groups, this book can be considered a fundamental reference in the area.'

    Source: Mathematical Reviews

    Review of previous edition:‘Researchers and graduate students working in related areas, such as algebraic geometry, algebraic group theory, or number theory will appreciate this book and find many deep ideas, results and technical tools that may be used in other branches of mathematics.'

    Source: Zentralblatt MATH

    '[This book] is devoted to the elucidation of the structure and classification of pseudo-reductive groups over imperfect fields, completing the program initiated by J. Tits, A. Borel and T. Springer in the last three decades of the last century … [it] is a remarkable achievement and the definitive reference for pseudo-reductive groups. It certainly belongs in the library of anyone interested in algebraic groups and their arithmetic and geometry.'

    Felipe Zaldivar Source: MAA Reviews (maa.org/press/maa-reviews)

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    Contents

    Contents
    References
    References
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