Torsors and Rational Points

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 & endorsements

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

Customer reviews

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