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.
| ISBN: | 9780521802376 |
| Publication date: | 5th July 2001 |
| Author: | Alexei Imperial College of Science, Technology and Medicine, London Skorobogatov |
| Publisher: | Cambridge University Press |
| Format: | Hardback |
| Pagination: | 196 pages |
| Series: | Cambridge Tracts in Mathematics |
| Genres: |
Number theory Geometry |