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  1. Home
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  3. Torsors and Rational Points
  • Cited by 170
Publisher:
Cambridge University Press
Online publication date:
May 2010
Print publication year:
2001
Online ISBN:
9780511549588
DOI:
https://doi.org/10.1017/CBO9780511549588
Subjects:
Mathematics (general), Mathematics, Real and Complex Analysis, Number Theory
Series:
Cambridge Tracts in Mathematics (144)
Information

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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