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Book synopsis

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.

Book details

Book category Books in English Mathematics & science Mathematics Number theory

• Full title: Torsors and Rational Points
• Author: Alexei N. Skorobogatov
• Language: English
• Binding: Hardback
• Number of pages: 196
• EAN: 9780521802376
• ISBN: 0521802377
• ID: 01330136
• Publisher: Cambridge University Press
• Weight: 415 g
• Dimensions: 229 × 152 × 14 mm
• Date of publishing: 05. July 2001

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