Torsors and Rational Points
Part of Cambridge Tracts in Mathematics
- Author: Alexei Skorobogatov, Imperial College of Science, Technology and Medicine, London
- 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.
Read more- 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
Reviews & endorsements
'… the book provides an excellent account of the subject for the non-expert.' T. Szamuely, Zentralblatt für Mathematik
See more reviews'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.
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