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Torsors and Rational Points

Torsors and Rational Points

Part of Cambridge Tracts in Mathematics

  • Date Published: July 2001
  • availability: Available
  • format: Hardback
  • isbn: 9780521802376

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  • 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.

    • Gives complete proofs of fundamental theorems alongside detailed discussions of the key examples
    • The first book about the Manin obstruction and applications of torsors to rational points
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    Reviews & endorsements

    '… the book provides an excellent account of the subject for the non-expert.' T. Szamuely, 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'. EMS

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    Product details

    • Date Published: July 2001
    • format: Hardback
    • isbn: 9780521802376
    • length: 196 pages
    • dimensions: 229 x 152 x 14 mm
    • weight: 0.46kg
    • availability: Available
  • Table of Contents

    1. Introduction
    2. Torsors: general theory
    3. Examples of torsors
    4. Abelian torsors
    5. Obstructions over number fields
    6. Abelian descent and Manin obstruction
    7. Conic bundle surfaces
    8. Bielliptic surfaces
    9. Homogenous spaces.

  • Author

    Alexei Skorobogatov, Imperial College of Science, Technology and Medicine, London

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