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  3. Torsors and Rational Points
  • Cited by 182
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    • Publisher:
      Cambridge University Press
      Publication date:
      May 2010
      July 2001
      ISBN:
      9780511549588
      9780521802376
      DOI:
      https://doi.org/10.1017/CBO9780511549588
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.46kg, 196 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Real and Complex Analysis, Number Theory
      Series:
      Cambridge Tracts in Mathematics (144)
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    Subjects:
    Mathematics (general), Mathematics, Real and Complex Analysis, Number Theory
    Series:
    Cambridge Tracts in Mathematics (144)
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    Book description

    The classical descent on curves of genus one can be interpreted as providing conditions on the set of rational points of an algebraic variety X defined over a number field, viewed as a subset of its adelic points. This is the natural set-up of the Hasse principle and various approximation properties of rational points. The most famous among such conditions is the Manin obstruction exploiting the Brauer-Grothendieck group of X. It emerged recently that a non-abelian generalization of descent sometimes provides stronger conditions on rational points. An all-encompassing 'obstruction' is related to the X-torsors (families of principal homogenous spaces with base X) under algebraic groups. This book, first published in 2001, is a detailed exposition of the general theory of torsors with key examples, the relation of descent to the Manin obstruction, and applications of descent: to conic bundles, to bielliptic surfaces, and to homogenous spaces of algebraic groups.

    Reviews

    ‘… the book provides an excellent account of the subject for the non-expert.’

    T. Szamuely Source: Zentralblatt für Mathematik

    'The book is written in a clear and lucid manner with detailed examples that balance the abstract theory with concrete facts. It is reasonably self-contained and can therefore be recommended to newcomers to the recent development of the descent'.

    Source: EMS

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